NCERT Solutions For Class 7 Maths Chapter 12

NCERT Solutions For Class 7 Maths Chapter 12 PDF Free Download

NCERT Solutions For Class 7 Maths Chapter 12 Algebraic Expressions are provided here so that students can check for the solutions for each question and resolve the difficulties faced while solving the question from NCERT class 7 maths book. These solutions for chapter 12, are available in downloadable PDF format so that students can download it and also learn these materials offline. These solutions are the worksheets for students to practice for the final exam.

Students of Class 7 are suggested to solve NCERT questions for chapter Algebraic Expressions, in order to strengthen the basics and be able to solve questions that are usually asked in the final exams. Among all chapters in class 7 maths subject, Algebraic Expressions is an important topic for the students, whose concepts are used in further studies. One needs to practice thoroughly the formulas and identities mentioned in chapter 12, to score well in the examination.

Class 7 Maths NCERT Solutions – Algebraic Expressions

BYJU’S  also offering algebraic expressions worksheets for class 7 pdf here are in a detailed manner and students can find solutions to all types of questions which will be asked in the main exams. These PDF solutions for the chapter, Algebraic Expressions, are prepared by our subject experts in accordance with CBSE syllabus (2018-2019) and NCERT curriculum, to assists students in their exam preparations.

The topics covered in chapter 12, Algebraic Expressions, of class 7 Maths are;

  • Algebraic Expressions
  • Terms of an Expression
  • Factors of a term and Coefficients
  • Like and unlike terms
  • Monomials, binomials, trinomials and polynomials
  • Addition and subtraction of Algebraic Expressions
  • Finding the value of Algebraic Expressions
  • Using Algebraic Expressions – Formulas and rule

Apart from practising solutions for chapter 12, Algebraic Expressions, students are advised to solve sample papers and previous year question papers, to get an idea of paper pattern and also marks contained by this chapter in the final exam. Students can also score good marks in the final exam of class 7 by practising these question papers.

NCERT Solutions For Class 7 Maths Chapter 12 Exercises

Exercise 12.1


Q1: Using arithmetic operations, constants and variables find the algebraic expressions of the cases given below:

(i) Numbers a and b both squared and added.

(ii) Number 5 added to three times the product of s and t.

(iii) One-fourth of the product of numbers m and n.

(iv) One-half of the sum of numbers a and b.

(v) Product of numbers e and f subtracted from 10.

(vi) Subtraction of v from u.

(vii) Sum of numbers s and t subtracted from their product

(viii) The number x multiplied by itself.

 

Sol:

(i) \(a^{2}+b^{2}\)

(ii) \(3st+5\)

(iii) \(\frac{mn}{4}\)

(iv) \(\frac{a+b}{2}\)

(v) \(10- ef\)

(vi) u-v

(vii) \(st-(s+t)\)

(viii) \(x^{2}\)

 

Q2:  

(a) Figure out the terms and their factors in the expression given below and show them by the help of tree diagram

(i) \(a-3\)

(ii) \(1+a+a^{2}\)

(iii) \(y-y^{3}\)  

(iv)\(5ab^{2}+7x^{2}y\)  

(v) \(-xy+2y^{2}-3x^{2}\)

 

(b) Figure out the terms and factors in the expressions below:

(i)  \(-4a+5\)

(ii) \(-4a+5b\)

(iii) \(5a+3a^{2}\)  

(iv) \(ab+2a^{2}b^{2}\)

(v) \(ab+b\)  

(vi) \(1.2xy-2.4y+3.6x\)  

(vii) \(\frac{3}{4}x+\frac{1}{4}\)

(viii) \(0.1a^{2}+0.2b^{2}\)

Also show the terms and factors by tree diagram.

 

Sol:

(a)

(i) \(a-3\)

(ii)   \(1+a+a^{2}\)

(iii) \(y-y^{3}\)

(iv)  \(5ab^{2}+7x^{2}y\)

(v)   \(-xy+2y^{2}-3x^{2}\)

 

(b)-

(i)   \(-4a+5\)

Terms:  \(-4a,5\)

Factors:  \( -4,\; a;\; 5\)

 

(ii) \(-4a+5b\)

Terms:  \(-4a,5b\)

Factors:   \(-4,\;a;\;5,\;b\)

 

(iii) \(5a+3a^{2}\)

Terms:  \(5a,3a^{2}\)

Factors:   \(5,\;a;\;3,\;a\;a\)

 

(iv) \(ab+2a^{2}b^{2}\)

Terms:  \(ab,2a^{2}b^{2}\)

Factors:   \(a,\;b;\;2,\;a,\;a;\;b,\;b\)

 

(v) \(ab+b\)

Terms:  \(ab,b\)

Factors:   \(a,\;b;\;b\)

 

(vi) \(1.2xy-2.4y+3.6x\)

Terms:  \(1.2xy,-2.4y,3.6x\)

Factors:   \(1.2,\;x,\;y;\;-2.4,\;y;\;3.6\; x\)

 

(vii) \(\frac{3}{4}x+\frac{1}{4}\)

Terms:  \(\frac{3}{4}x,\frac{1}{4}\)

Factors:   \(\frac{3}{4},\;x;\; \frac{1}{4}\)

 

(viii) \(0.1a^{2}+0.2b^{2}\)

Terms:  \(0.1a^{2},0.2b^{2}\)

Factors:   \(0.1,\;a,\;a;\;0.2,\;b\;b\)

 

Q3: Other than the constants figure out the numerical coefficients of the given expressions:

(i) \(5-3a^{2}\)

(ii)  \(1=a+a^{2}+a^{3}\)

(iii) \(a+2ab+3b\)

(iv) \(100x+100y\)

(v) \(-x^{2}y^{2}+7xy\)

(vi) \(1.2x+0.8y\)

(vii) \(3.14x^{2}\)

(viii) \(2(a+b)\)

(ix) \(0.1x+0.01x^{2}\)

 

S.no Expression Terms Numerical Coefficient
(i) \(5-3a^{2}\) \(-3a^{2}\)
(ii) \(1=a+a^{2}+a^{3}\)  

a
\(a^{2}\)
\(a^{3}\)
 

1
1
1
(iii) \(a+2ab+3b\)  

a
2ab
3b
 

1
2
3
(iv) \(100x+100y\)  

100m
100n
 

100
100
(v) \(-x^{2}y^{2}+7xy\)  

\(-x^{2}y^{2}\)
\(7xy\)
 

-1
7
(vi) \(1.2x+0.8y\)  

\(1.2x\)
\(0.8y\)
 

1.2
0.8
(vii) \(3.14x^{2}\) \(3.14x^{2}\) 3.14
(viii) \(2(a+b)\)  

2a
2b
 

2
2
(ix) \(0.1x+0.01x^{2}\)  

\(0.1x\)
\(0.01x^{2}\)
 

0.1
0.01

 

Q4:

(a) Identify the terms which contain ‘a’ and give the coefficient of a.

 

(i) \(b^{2}a+b\)

(ii) \(13b^{2}-8ab\)

(iii) \(a+b+15\)

(iv) \(5+m+ma\)

(v) \(1+a+ab\)

(vi) \(12ab^{2}+10\)

(vii) \(7a+am^{2}\)

 

(b) Figure out the terms which contain \(b^{2}\) and also give the coefficient of the same term.

(i) \(8-ab^{2}\)

(ii) \(5b^{2}+10a\)

(iii) \(2a^{2}b-5ab^{2}+15b^{2}\)

 

Sol:

 

S.no Expression Terms with factor a Coefficient of a
(i) \(b^{2}a+b\) \(b^{2}a\) \(b^{2}\)
(ii) \(13b^{2}-8ab\) \(-8ab\) \(-8b\)
(iii) \(a+b+15\) a 1
(iv) \(5+m+ma\) ma m
(v) \(1+a+ab\)  

a
ab
 

1
b
(vi) \(12ab^{2}+10\) \(12ab^{2}\) \(12b^{2}\)
(vii) \(7a+am^{2}\)  

\(am^{2}\)
7a
 

\(m^{2}\)
7

 

(b)

 

S.no Expression Terms containing \(b^{2}\) Coefficient of \(b^{2}\)
(i) \(8-ab^{2}\) \(-ab^{2}\) \(-a\)
(ii) \(5b^{2}+10a\) \(5b^{2}\) 5
(iii) \(2a^{2}b-5ab^{2}+15b^{2}\)  

\(-5ab^{2}\)
\(15b^{2}\)
 

\(-5a\)
15

 

Q5: Classify into monomials, binomials and trinomials:

(i) \(4b-7a\)

(ii) \(b^{2}\)

(iii) \(a+b-ab\)

(iv) \(50\)

(v) \(ab+b+a\)

(vi) \(5+10x\)

(vii) \(15a^{2}b-10ab^{2}\)

(viii) \(10yz\)

(ix) \(x^{2}+10x-5\)

(x) \(x^{2}+y^{2}\)

(xi) \(x^{2}+y\)

(xii) \(a^{2}+a+50\)

 

Sol:

 

S.no Expression Type of Polynomial
(i) \(4b-7a\) Binomial
(ii) \(b^{2}\) Monomial
(iii) \(a+b-ab\) Trinomial
(iv) \(50\) Monomial
(v) \(ab+b+a\) Trinomial
(vi) \(5+10x\) Binomial
(vii) \(15a^{2}b-10ab^{2}\) Binomial
(viii) \(10yz\) Monomial
(ix) \(x^{2}+10x-5\) Trinomial
(x) \(x^{2}+y^{2}\) Binomial
(xi) \(x^{2}+y\) Binomial
(xii) \(a^{2}+a+50\) Trinomial

 

Q6: State whether a given pair of term is of like or unlike terms:

(i) 1,100

(ii) \(-20x, \frac{1}{2}x\)

(iii) \(-10x, -10 y\)

(iv) \(50ab,30ba\)

(v) \(2 a^{2}b,8ab^{2}\)

(vi) \(10ab, 20 a^{2}b\)

 

Sol:

 

S.no Pair of terms Like/Unlike terms
(i) 1,100 Like terms
(ii) \(-20x, \frac{1}{2}x\) Like terms
(iii) \(-10x, -10 y\) Unlike terms
(iv) \(50ab,30ba\) Like terms
(v) \(2 a^{2}b,8ab^{2}\) Unlike terms
(vi) \(10ab, 20 a^{2}b\) Unlike terms

 

Q7: Identify the like terms in the following:

(a) \(-a^{2}b,-4ab^{2},9a^{2},2ab^{2},10a,-20a^{2},-30a, -5a^{2}b,-2ab,35a\)

(b) \(10pq,10p,5q,2p^{2}q^{2},-5pq,-50q,-30,18p^{2}q^{2},55,100p,-30pq, 105p^{2}q,-200\)

 

Sol:

(a) Like terms are:

(i) \(-a^{2}b, -5a^{2}b\)

(ii) \(-4ab^{2}, 2ab^{2}\)

(iii) \(9a^{2},-20a^{2}  \)

(iv) \(10a,-30a,35a\)

(v) \(-2ab \)

 

(b) Like terms are:

(i)  \(10pq,-5pq,-30pq \)

(ii)  \( 10p,100p,\)

(iii) \(5q, -50q \)

(iv) \(2p^{2}q^{2}, 18p^{2}q^{2}\)

(v) \(-30, 55,-200\)

(vi) \(105p^{2}q \)

 

Exercise 12.2


 

Q1: Simplify the terms:

(i) \(21a-32+7a-20a\)

(ii) \(-x^{2}+13x^{2}-5x+7x^{3}-15x\)

(iii) \(a-(a-b)-b-(b-a)\)

(iv) \(3x-2y-xy-(x-y+xy)+3xy+y-x\)

(v) \(5a^{2}b-5a^{2}+3a^{2}b-3b^{2}+a^{2}-b^{2}+8ab^{2}-3b^{2}\)

(vi) \((3b^{2}+5b-4)-(8b-b^{2}-4)\)

Sol:

(i) \(21a-32+7a-20a=21a+7a-20b-32\) \(\Rightarrow 8b-32\)

 

(ii) \(-x^{2}+13x^{2}-5x+7x^{3}-15x=7x^{3}+13x^{2}-x^{2}-5x-15x\) \(=7x^{3}+12x^{2}-20x\)

 

(iii) \(a-(a-b)-b-(b-a)=a-a+b-b-b+a\) \(=a-b\)

 

(iv) \(3x-2y-xy-(x-y+xy)+3xy+y-x=3x-2y-xy-x+y-xy+3xy+y-x\) \(=3x-x-x+y+y-2y-xy-xy+3xy\) \(=x-2xy+3xy\)

 

(v)  \(5a^{2}b-5a^{2}+3a^{2}b-3b^{2}+a^{2}-b^{2}+8ab^{2}-3b^{2}\) \(5a^{2}b+3a^{2}b+8ab^{2}-5a^{2}+a^{2}-3b^{2}-b^{2}-3b^{2}=8a^{2}b+8ab^{2}-4a^{2}-7b^{2}\)

 

(vi) \((3b^{2}+5b-4)-(8b-b^{2}-4)\) \(3b^{2}+5b-4-8b+b^{2}+4=3b^{2}+b^{2}+5b-8b+4-4\) \(=4b^{2}-3b\)

 

Q2: Add:

(i) \(3mn,-5mn,8mn,-4mn\)

(ii) \(a-8ab,3ab-b,b-a\)

(iii) \(-7mn+5,12mn+2, 9mn-8, 2mn-3\)

(iv) \(a+b-3,b-a+3,a-b+3\)

(v) \(14x+10y-12xy-13,18-7x-10y+8xy,4xy\)

(vi) \(5m-7n,3n-4m+2,2m-3mn-5\)

(vii) \(4x^{2}y,-3xy^{2},-5xy^{2},5x^{2}y\)

(viii) \(3p^{2}q^{2}-4pq+5,-10p^{2}q^{2},15+9pq+7p^{2}q^{2}\)

(ix) \(ab-4a,4b-ab,4a-4b\)

(x) \(x^{2}-y^{2}-1,y^{2}-1-x^{2},1-x^{2}-y^{2}\)

Sol:

(i) \(3mn,-5mn,8mn,-4mn\) \(3mn+(-5mn)+8mn(-4mn)=(3-5+8-4)mn\) \(=(2)mn\)

 

(ii) \(a-8ab,3ab-b,b-a\) \(a-8ab+3ab-b+b-a=a-a+b-b-8ab+3ab\) \(=-5ab\)

 

(iii) \(-7mn+5,12mn+2, 9mn-8, 2mn-3\) \(-7mn+5+12mn+2+9mn-8+2mn-3=-7mn+12mn+9mn+5+2-8-3\) \(=(-7+12+9)mn+(5+2-8-3)=14mn+2\)

 

(iv) \(a+b-3,b-a+3,a-b+3\) \(a+b-3+b-a+3+a-b+3=a+a-a+b+b-b+3+3-3\) \(=(1+1-1)a+(1+1-1)b+(3+3-3)=a+b+3\)

 

(v) \(14x+10y-12xy-13,18-7x-10y+8xy,4xy\) \(=14x-7x+10y-10y+8xy+4xy-12xy+18-13=7x+18\) \(=7x+18\)

 

(vi) \(5m-7n,3n-4m+2,2m-3mn-5\) \(5m-4m+2m-7n+3n+2-5-3mn=3m-4n-3mn-3\)

 

(vii) \(4x^{2}y,-3xy^{2},-5xy^{2},5x^{2}y\) \(4x^{2}y+(-3xy^{2})+(-5xy^{2})+5x^{2}y=4x^{2}y+5x^{2}y-3xy^{2}-5xy^{2}\) \(=9x^{2}y-8xy^{2}\)

 

(viii) \(3p^{2}q^{2}-4pq+5,-10p^{2}q^{2},15+9pq+7p^{2}q^{2}\) \(3p^{2}q^{2}-4pq+5+(-10p^{2}q^{2})+15+9pq+7p^{2}q^{2}=3p^{2}q^{2}+7p^{2}q^{2}-10p^{2}q^{2}+9pq-4pq+15-5\) \(=5pq+10\)

 

(ix) \(ab-4a,4b-ab,4a-4b\) \(ab-4a+4b-ab+4a-4b=4a-4a+4b-4b+ab-ab\) \(=0\)

 

(x) \(x^{2}-y^{2}-1,y^{2}-1-x^{2},1-x^{2}-y^{2}\) \(x^{2}-y^{2}-1+y^{2}-1-x^{2}+1-x^{2}-y^{2}=x^{2}-x^{2}-x^{2}+y^{2}-y^{2}-y^{2}+1-1-1\) \(=-x^{2}-y^{2}-1\)

 

Q3: Subtract:

(i)  \(-5y^{2}\) from \(y^{2}\)

(ii) \(6xy\) from \(-12xy\)

(iii) \((a-b)\) from \((a+b)\)

(iv) \(a(b-5)\) from \(b(5-a)\)

(v) \(-m^{2}+5mn\) from \(4m^{2}-3mn+8\)

(vi) \(-x^{2}+10x-5\) from \(5x-10\)

(vii) \(5a^{2}-7ab+5b^{2}\) from \(3ab-2a^{2}-2b^{2}\)

(viii) \(4pq-5q^{2}-3p^{2}\) from \(5p^{2}+3q^{2}-pq\)

 

Sol:

(i) \(y^{2}-(-5y^{2})\)

    \(=y^{2}+5y^{2}\) \(=6y^{2}\)

 

(ii) \(-12xy-6xy\) \(=-18xy\)

 

(iii) \((a+b)-(a-b)\) \(=a+b-a+b\) \(=2b\)

 

(iv) \(b(5-a)-a(b-5)\) \(=5b-ab-ab+5a\) \(=5a+5b-2ab\)

 

(v)  \(4m^{2}-3mn+8-(-m^{2}+5mn)\) \(=4m^{2}-3mn+8+m^{2}-5mn\) \(=5m^{2}-8mn+8\)

 

(vi) \(5x-10-(-x^{2}+10x-5)\) \(=5x-10+x^{2}-10x+5\) \(=x^{2}-5x-5\)

 

(vii) \(3ab-2a^{2}-2b^{2}-(5a^{2}-7ab+5b^{2})\) \(=3ab-2a^{2}-2b^{2}-5a^{2}+7ab-5b^{2}\) \(=3ab+7ab-2a^{2}-5a^{2}-2b^{2}-5b^{2}\) \(=10ab-7a^{2}-7b^{2}\)

 

(viii) \(5p^{2}+3q^{2}-pq-(4pq-5q^{2}-3p^{2})\) \(=5p^{2}+3q^{2}-pq-4pq+5q^{2}+3p^{2}\) \(=5p^{2}+3p^{2}+3q^{2}+5q^{2}-pq-4pq\) \(=8p^{2}+8q^{2}-5pq\)

 

Q4: (a) What should be added to \(x^{2}+xy+y^{2}\) to obtain \(2x^{2}+3xy\) ?

(b) What should be subtracted from \(2a+8b+10\) to get \(-3a+7b+16\)?

 

Sol:

(a) Let a should be added

Then according to the question

\(x^{2}+xy+y^{2}+a=2x^{2}+3xy\)

 

\(\Rightarrow a=2x^{2}+3xy-(x^{2}+xy+y^{2})\)

 

\(\Rightarrow a=2x^{2}+3xy-x^{2}-xy-y^{2}\)

 

\(\Rightarrow a=2x^{2}-x^{2}-y^{2}+3xy-xy\)

 

\(\Rightarrow a=x^{2}-y^{2}+2xy\)

Hence the value of a comes out to be \(x^{2}-y^{2}+2xy\).

Hence  \(x^{2}-y^{2}+2xy\) should be added.

 

(b) Let b should be subtracted

Then according to the question,

\(2a+8b+10-q= -3a+7b+16\)

 

\(2a+8b+10-q= -3a+7b+16\)

 

\( q = 2a+8b+10-( -3a+7b+16)\)

 

\( q = 2a+8b+10+3a-7b-16\)

 

\( q = 2a+3a+8b-7b+10-16\)

 

\( q = 5a+b-6\)

 

Q5: What should be taken from 3x2-4y2+5xy+20 to obtain –x2-y2+6xy+20 ?

Sol:

Let a be subtracted

Then according to the question,

3x-4y2+5xy+20 – q= –x2-y2+6xy+20

q=  3x-4y2+5xy+20 -(–x2-y2+6xy+20)

q= 3x2-4y2+5xy+20+x2+y2-6xy-20

q=3x2+x2-4y2+y2+5xy-6xy +20 -20

q=4x2-3y2-xy

Hence, 4x2-3y2-xy should be subtracted in the given equation.

 

Q6:

(a) From the sum of 3x – y + 11 and – y – 11, subtract 3x – y – 11.

(b) From the sum of 4 + 3x and 5 – 4x + 2x, subtract the sum of 3x2 – 5x and –x2 + 2x + 5.

Sol:

(a)According to the question

(3x – y + 11)+( – y – 11)-( 3x – y – 11)= 3x – y + 11 – y – 11- 3x + y + 11

= 3x-3x+y-y+11+11-11

=11

(b) According to question,

(4 + 3x)+( 5 – 4x + 2x2)-( 3x2 – 5x)-( –x2 + 2x + 5)

= 4 + 3x+ 5 – 4x + 2x2– 3x2 + 5x +x2 – 2x – 5

= 3x-4x+5x-2x +2x2– 3x2+x2+4+5-5

= 2x+4

 

Exercise 12.3


Q1: If a=2, find the values of:

(i) a-2

(ii) 3a-5

(iii) 9-5a

(iv) \(3a^{2}-2a-7\)

(v) \(\frac{5m}{2}-4\)

 

Sol:

(i) a-2 =2-2  (Putting a=2)

=0

 

(ii)  3a-5= \(3\times 2-5\)   (Putting a=2)

=1

 

(iii)   9-5a=\(9-5\times 2\) (Putting a=2)

= -1

 

(iv)  \(3a^{2}-2a-7=3\times 2^{2}-2\times 2-7\)  (Putting a=2)

=12-4-7

=1

 

(v)  \(\frac{5m}{2}-4 =\frac{5\times 2}{2}-4 =5-4\)   (Putting a=2)

=1

 

Q2: If x=-2, find

(i)  4x+7

(ii)  \(-3x^{2}+4x+7\)

(iii) \(-2x^{3}-3x^{2}+4x+7\)

 

Sol:

(i)  4x+7=4(-2)+7   (Putting x= -2)

= -8+7=-1

 

(ii)  \(-3x^{2}+4x+7=-3(-2)^{2}+4(-2)+7\)

= -3(4)-8+7=-12-8+7

= -13

 

(iii) \(-2x^{3}-3x^{2}+4x+7=-2(-2)^{3}-3(-2)^{2}+4(-2)+7\)  (Putting x= -2)

= -2(-8)-3(4)+4(-2)+7

=  16-12-8+7

=3

 

Q3: Find the value of the following expressions, when x= -1:

(i) 5x-35

(ii) -2x+4

(iii) \(3x^{2}+6x+3\)

(iv) \(6x^{2}-3x-6\)  

Sol:

(i) 5x-35 = 5(-1)-35 =-5-35              [Putting x= -1 ]

= -40

(ii)  -2x+4  = -2(-1)+4            [Putting x= -1 ]

= 2 + 4 = 6

(iii) \(3x^{2}+6x+3\) = \(3(-1)^{2}+6(-1)+3\)      [Putting x= -1 ]

= 3-6+3 =0

(iv) \(6x^{2}-3x-6\)  = \(6(-1)^{2}-3(-1)-6\)        [Putting x= -1 ]

= 6+1-6 =1

 

Q 4: If x=2, y= -2, find the value of:

(i) \(x^{2}+y^{2}\)  

(ii) \(x^{2}+xy+y^{2}\)  

(iii) \(x^{2}-y^{2}\)

 

Sol:

(i) \(x^{2}+y^{2}\) = \(2^{2}+(-2)^{2}\)                        [Putting a=2,  b= -2 ]

= 4 + 4 = 8

(ii) \(x^{2}+xy+y^{2}\)  = \(2^{2}+2(-2)+(-2)^{2}\)        [Putting a=2,b= -2 ]

= 4 – 4 + 4 = 4

(iii) \(x^{2}-y^{2}\) = \((2)^{2}-(-2)^{2}\)                        [Putting a=2, b= -2]

= 4 – 4 = 0

 

Q5: When x=0,y= -1, find the value of the given expressions:

(i) 2x+2y

(ii) \(2x^{2}+y^{2}+1\)  

(iii) \(2x^{2}y+2xy^{2}+xy\)

(iv) \(x^{2}+xy+2\)

Sol:

(i) 2x+2y = 2(0)+2(-1)     [Putting x=0,y= -1 ]

= 0 – 2 = -2

(ii) \(2x^{2}+y^{2}+1\) = \(2(0)^{2}+(-1)^{2}+1\)   [Putting x=0, y=-1 ]

= 0 + 1 + 1 = 2

(iii) \(2x^{2}y+2xy^{2}+xy\) =  \(2(0)^{2}(-1)+2(0)(-1)^{2}+0(-1)\)      [Putting x=0, y= -1]

= 0 + 0 + 0 = 0

(iv) \(x^{2}+xy+2\) = \((0)^{2}+(0)(-1)+2\)    [Putting x=0, y= -1 ]

= 0 + 0 + 2 = 2

 

Q6: Simplify the following expressions and find the value at a= 2:

(i) a+7+4(a-5)

 (ii) 3(a+2)+5a-7  

(iii) 10a+4(a-2)

(iv) 5(3a-2)+4a+8    

 

Sol:

(i) a+7+4(a-5) = a+7+4a-20

=4a+a+7-20 =5a-13

= 5(2)-13 =10-13                                                                                   [Putting a=2 ]

= -3

 

(ii) 3(a+2)+5a-7 = 3a+6+5a-7

= 3a+5a+6-7  = 8a-1

= 8( 2) – 1                                                                                               [Putting a=2 ]

= 16 – 1 = 15

 

(iii) 10a+4(a-2) = 10a+4a-8

= 14a-8

= 14( 2) – 8                                                                                            [Putting a= 2 ]

= 28 – 8 = 20

 

(iv) 5(3a-2)+4a+8 = 15a-10+4a+8

=15a+4a-10+8 = 19a-2                                                                           [Putting =2  ]

= 19(2)-2 = 38-2

= 36

 

Q7: Simplify the expression given below and find the value at x=3, y= -1, z= -2  :

(i) 8x-10-3x+5

(ii) 10-5x+3x+6

(iii) 5y+3-2y+6

(iv) 5-8z-12-4z

(v) 3y-5z-6x+15

Sol:

(i) 8x-10-3x+5 = 8x-3x-10+5

=5x-5 = 5(3)-5                                                                                                [Putting x=3 ]

= 15-5 = 0

(ii) 10-5x+3x+6 = 10+6-5x+3x

= 16-2x = 16-2(3)                                                                                           [Putting x= 3 ]

=  16-6 =10

(iii) 5y+3-2y+6 = 5y-2y+3+6

= 3y+9 = 3(-1)+9                                                                                             [Putting y= -1 ]

= -3 + 9 = 6

(iv) 5-8z-12-4z = 5-12-8z-4z

= -7-12 z                                                                                                         [Putting z= -2 ]

= -7 -12(-2) = -7+24

= 17

(v) 3y-5z-6x+15

= 3(-1)-5(-2)-6(3)+15                                                                       [Putting x=3, y=-1, z=-2]

= -3+10-18+15

= 25-21

= 4

 

Q8:

(i) If x= 10, find the value of \(x^{3}-3x^{2}-5x+15\) .

(ii) If y= -10, find the value of \(2y^{2}-3y+50\)

 

Sol:

(i) \(x^{3}-3x^{2}-5x+15\)

= \(10^{3}-3(10)^{2}-5(10)+15\)                                                   [Putting x=10 ]

=1000-300-50+15

= 665

 

(ii) \(2y^{2}-3y+50\)

=\(2(-10)^{2}-3(-10)+50\)                                                            [Putting y= -10 ]

=200+30+50

=280

 

Q9: What should be the value of p if the value of \(2a^{2}+a-p=5\) equals to 5, when a=0 ?

Sol:

\(2a^{2}+a-p=5\) \(2(0)^{2}+0-p=5\)                                                                         [ Putting x= 0 ] \(-p=5\)

Hence, the value of p is -5.

 

Q10: Simplify the expression and find its value when x= 5 and y= -3:   

\(2(x^{2}+xy)+3-xy\).

Sol:

 

Given:

\(2(x^{2}+xy)+3-xy\)

 

\(\Rightarrow 2x^{2}+2xy+3-xy\)

 

\(\Rightarrow 2x^{2}+2xy-xy+3\)

 

\(\Rightarrow 2x^{2}+xy+3\)

 

\(\Rightarrow 2(5)^{2}+(5)(-3)+3\)             [Putting x=5, y= -3 ]

 

\(\Rightarrow 2(25)+(-15)+3\)

 

\(\Rightarrow 50-15+3\) \(\Rightarrow 38\)

 

Exercise 12.4


Q1: Observe the pattern made from the line segment, which are of equal length which are found in display of calculators and digital speedometer: If n is the number of digits, and the number of required segments to form the digit n is given by the algebraic expression on the right of the digit. So how many segments are required to form 5,10,100 digits of the kind .

Sol:

 

S.no Symbols Digit’s number Pattern Formulae No. of segments
(i)  

5
10
100
\(5n+1\)  

26
51
501
(ii)  

5
10
100
\(3n+1\)  

16
31
301
(iii)  

5
10
100
\(5n+2\)  

27
52
502

 

(i) \(5n+1\)

Putting n=5,          \(5\times 5+1=25+1=26\)

Putting n=10,        \(5\times 10+1=50+1=51\)

Putting n=100,       \(5\times 100+1=500+1=501\)

 

(ii) \(3n+1\)

Putting n=5,          \(3\times 5+1=15+1=16\)

Putting n=10,        \(3\times 10+1=30+1=31\)

Putting n=100,        \(3\times 100+1=300+1=301\)

 

(iii) \(5n+2\)

Putting n=5,          \(5\times 5+2=25+2=27\)

Putting n=10,        \(5\times 10+2=50+1=52\)

Putting n=100,       \(5\times 100+2=500+1=502\)

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