ICSE Class 8 Maths Selina Solutions Chapter 11 Algebraic Expressions

The ICSE Class 8 Selina Solutions are very helpful for the students especially when they are preparing for the annual exams. Many times students are not able to solve the problems provided in the exercise. So, they need some authentic resources from where they can see the solutions and understand them. To help students with this we have provided the ICSE Class 8 Maths Selina Solutions.

Chapter 11 of ICSE Class 8 Maths covers the Algebraic Expressions. In this chapter, students will study how to find the coefficients and degree of a polynomial, addition and subtraction of polynomials and few word problems related to it. Here we have provided the step by step solution to all the questions in PDF format for ICSE Class 8 Maths Selina Solutions Chapter 11 Algebraic Expressions. Going through it students can easily understand the solution. To access the pdf click on the download link below;

Download ICSE Class 8 Maths Selina Solutions Chapter 11 Algebraic Expressions

ICSE Class 8 Maths Chapter 11 Algebraic Expressions has only 8 Questions. The solutions to all these questions are also provided below:

ICSE Class 8 Maths Selina Solutions Chapter 11 – Algebraic Expressions

Question 1. Separate the constants and variables from the following:

\( -7,7+x, 7 x+y z, \sqrt{5}, \sqrt{x y}, \frac{3 y z}{8}, 4.5 y-3 x\) \( 8-5,8-5 x, 8 x-5 y \times p \text { and } 3 y^{2} z \div 4 x\)

Solution:-

Clearly constants are: \( -7, \sqrt{5}, 8-5 \)

Variable are: \( 7+x, 7 x+y z, \sqrt{x y}, \frac{3 y z}{8}, 4.5 y-3 x\) \( 8-5 x, 8 x-5 y \times p \text { and } 3 y^{2} z \div 4 x\)

Question 2.

Write the number of terms in each of the following polynomials.

(i) \( 5 x^{2}+3 x a x \) \( 5 x^{2}+3 \times a x=5 x^{2}+3 a x\)

∴ The number of terms in this Polynomial =2

(ii) \( a x \div 4-7=\frac{a x}{4}-7 \)

∴ The number of terms in this polynomial =2

(iii) \( a x-b y+y \times z=a x-b y+y z \)

∴ The number of terms in this polynomial =3

(iv) \( 23+a \times b \div 2=23+\frac{a b}{2} \)

∴ The number of terms in this polynomial =2

Question 3.

Separate monomials, binomials, trinomials and polynomials from the following algebraic expressions:

\( 8-3 x, x y^{2}, 3 y^{2}-5 y+8,9 x-3 x^{2}+15 x^{3}-7\) \( 3 x \times 5 y, 3 x \div 5 y, 2 y \div 7+3 x-7 \text { and } 4-a x^{2}+b x+y\)

Solution:-

Monomials are: \( x y^{2}, 3 x \times 5 y, 3 x \div 5 y\)

Binomials are: 8-3 x

Trinomials are: \( 3 y^{2}-5 y+8,2 y \div 7+3 x-7\)

Polynomials are: \( 8-3 x, 3 y^{2}-5 y+8,9 x-3 x^{2}+15 x^{3}-7,2 y \div 7+3 x-7,4-a x^{2}+b x+y\)

Question 4.

Write the degree of each polynomial given below:

(i) x y+7 z

Solution:-

degree=2(Polynomial is xy+7z)

(ii) \( x^{2}-6 x^{3}+8 y\)

Solution:-

Degree=3(Polynomial is \( x^{2}-6 x^{3}+8 y )\)

(iii) \( y-6 y^{2}+5 y^{8} \)

Solution:-

Degree= 8 (Polynomial is \( y-6 y^{2}+5 y^{8}) \)

(iv) x y z-3

Solution:-

Degree=3 (Polynomial is xyz-3)

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

Solution:-

Degree= (Polynomial is \( x y+y z^{2}-x z^{3})\)

(vi) \( x^{5} y^{7}-8 x^{3} y^{8}+10 x^{4} y^{4} z^{4}\)

Degree= 12 (Polynomial is \( x^{5} y^{7}-8 x^{3} y^{8}+10 x^{4}, y^{4} z^{4}) \)

Question 5.

Write the coefficient of:

(i) ab in 7abx

Solution:-

The coefficient of ab in 7 a b x=7 x

(ii) 7a in 7abx

Solution:-

The coefficient of ab 7a in 7abx=bx

(iii) \( 5 x^{2} \text { in } 5 x^{2}-5 x \)

Solution:-

The coefficient of \( 5 x^{2} \text { in } 5 x^{2}-5 x=1 \)

(iv) \( 8 \text { in } a^{2}-8 a x+a\)

Solution:-

The coefficient of 8 in \( a^{2}-8 a x+a=-a x \)

(v) \( 4 x y \text { in } x^{2}-4 x y+y^{2}\)

Solution:-

The coefficient of \( 4 x y \text { in } x^{2}-4 x y+y^{2}=-1\)

Question 6:

\( \ln \frac{5}{7} x y^{2} z^{3}\) . Write the coefficient of

(i) 5

Solution:-

\( 5 \text { is } \frac{1}{7} x y^{2} z^{3}\)

(ii) \( \frac{5}{7}\)

Solution:-

\( \frac{5}{7} \text { is } x y^{2} z^{3}\)

(iii) 5 x

\( 5 x \text { is } \frac{1}{7} y^{2} z^{3}\)

(iv) \(x y^{2} \)

Solution:-

\( x y^{2} \text { is } \frac{5}{7} z^{3}\)

(v) \(z^{3}\)

Solution:-

\( z^{3} \text { is } \frac{5}{7} x y^{2}\)

(vi) \(x z^{3} \)

Solution:-

\( x z^{3} \text { is } \frac{5}{7} y^{2}\)

(vii) \(5 x y^{2}\)

Solution:-

\( 5 x y^{2} \text { is } \frac{1}{7} z^{3}\)

(viii) \( \frac{1}{7} y z \)

Solution:-

\( \frac{1}{7} y z \text {is} 5 x y z^{2}\)

(ix) z

Solution:-

\( z \text { is } \frac{5}{7} x y^{2} z^{2}\)

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

Solution:-

\( y z^{2} \text { is } \frac{5}{7} x y-z\)

(xi) 5 xyz

Solution:-

\( 5 x y z \text { is } \frac{1}{7} y z^{2}\)

Question 7.

In each polynomial, given below, separate the like terms:

(i) \( 3 x y,-4 y x^{2}, 2 x y^{2}, 2.5 x^{2} y,-8 y x,-3.2 y^{2} x \text { and } x^{2} y\)

Solution:-

(i) Like terms are

\( 3 x y,-8 y x \cdot-4 y x^{2}, 2.5 x^{2} y \text { and } x^{2} y ; 2 x y^{2} \text { and }-3.2 y^{2}\)

(ii) \( y^{2} z^{3}, x y^{2} z^{3},-5 x^{2} y z,-4 y^{2} z^{3},-8 x z^{3} y^{2}, 3 x^{2} y z \text { and } 2 z^{3} y^{2}\)

Solution:-

\( y^{2} z^{3},-y^{2} z^{3} \text { and } 2 z^{3} y^{2} ; x y^{2} z^{3} \text { and }-8 x z^{3} y-5 x^{2} y z \text { and } : x^{2} y z\)

Question 8.  

Evaluate: 

(i) \( -7 x^{2}+18 x^{2}+3 x^{2}-5 x^{2}\)

Solution:-

\( =21 x^{2}-12 x^{2}\) \( =9 x^{2}\)

(ii) \( b^{2} y-9 b^{2} y+2 b^{2} y-5 b^{2} \} \)

Solution:-

\( =3 b^{2} y-14 b^{2} y\) \( =-11 b^{2} y\)

(iii) abx-15abx-10abx+32abx

Solution:-

=33abx-25abx

=8abx

(iv) 7x-9y+3-3x-5y+8

Solution:-

=7x-3x-9y-5y+3+8

=4x-14y+11

(v) \( 3 x^{2}+5 x y-4 y^{2}+x^{2}-8 x y-5 y^{2}\)

Solution:-

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

Question 9 

Add :

(i) 5a+3y . a-2b,3a+5b

Solution:-

ICSE Class 8 Maths Selina Solutions for Chapter 11-1

(ii)8x-3y+7z,-4x+5y-4z,-x-y-2z
Solution:

ICSE Class 8 Maths Selina Solutions for Chapter 11-2

(iii)3b-7c+10,5c-2b-15,15+12c+b

Solution:-

ICSE Class 8 Maths Selina Solutions for Chapter 11-3

(iv) a-3b+3;2a+5-3c:6c-15+6b

Solution:-

ICSE Class 8 Maths Selina Solutions for Chapter 11-4

(v)13ab-9cd-xy;5xy;15cd-7ab 6xy-3cd

ICSE Class 8 Maths Selina Solutions for Chapter 11-5Solution:

(vi) \( x^{3}-x^{2} y+5 x y^{2}+y^{3} ;-x^{3}-9 x y^{2}+y^{3} ; 3 x^{2} y+9 x y^{2} \)

Solution:

ICSE Class 8 Maths Selina Solutions for Chapter 11-6

(vii) \( a^{6}-4a^{4}+6a\);
\(5a^{6}+5a^{4}+6a\);
\(12a^{6}-10a\)

Solution:-

ICSE Class 8 Maths Selina Solutions for Chapter 11-7

(viii) \( 2ax-6by+4cz\);
\(4by-14ax\);
\(9cz-4ax-6by\)

Solution:-

ICSE Class 8 Maths Selina Solutions for Chapter 11-8

Question 3

Find the total savings of a boy who saves £ (4x-6y); £ (6x+2y); £ (4y-x)and £ (y-2x)for four consecutive weeks.

Solution:-

ICSE Class 8 Maths Selina Solutions for Chapter 11-9

∴Total savings= (7x+y)

Question 4.

Subtract:

(i) \( 4 x y^{2} \text { from } 3 x y^{2} \)

Solution:-

\( 3 x y^{2}-4 x y^{2}=-x y^{2}\)

(ii) \( -2 x^{2} y+3 x y^{2} \text { from } 8 x^{2} y \)

Solution:-

ICSE Class 8 Maths Selina Solutions for Chapter 11-10

(iii) 3a-5b+c+2d from 7a-3b+c-2d

Solution:-

ICSE Class 8 Maths Selina Solutions for Chapter 11-11

(iv) \( x^{3}-4 x-1 \text { from } 3 x^{3}-x^{2}+6 \)

Solution:-

ICSE Class 8 Maths Selina Solutions for Chapter 11-12

(v) \( 6 a+3 \text { from } a^{3}-3 a^{2}+4 a+1\)

Solution:-

ICSE Class 8 Maths Selina Solutions for Chapter 11-13

(vi) cab-4cad-cbd from 3abc+5bcd-cda

Solution:-

ICSE Class 8 Maths Selina Solutions for Chapter 11-14

(vii) \( a^{2}+a b+b^{2} \text { from } 4 a^{2}-3 a b+2 b^{2}\)

Solution:-

ICSE Class 8 Maths Selina Solutions for Chapter 11-15

Question 5. 

(i) Take a \( 3 x^{3}+4 x^{2}-5 x+6 \text { from } 3 x-4 x^{2}+5 x-6 ) \)

Solution:-

ICSE Class 8 Maths Selina Solutions for Chapter 11-16

(ii)Take \( m^{2}+m+4 \text { from }-m^{2}+3 m+6 and the result from m^{2}+m+1\)

Solution:-

ICSE Class 8 Maths Selina Solutions for Chapter 11-17

Question 6.  

Subtract the sum of \( 5 y^{2}+y-3 \text { and } y^{2}-3 y+7 \text { from } 6 y^{2}+y-2\)

Solution:-

ICSE Class 8 Maths Selina Solutions for Chapter 11-18

Question: 7

What must be added \( x^{4}-x^{3}+x^{2}+x+3 \text { to obtain } x^{4}+x^{2}-1\) ?

Solution:-

ICSE Class 8 Maths Selina Solutions for Chapter 11-19

Question: 8

(i) How much more than \( 2 x^{2}+4 x y+2 y^{2} \text { is } 5 x^{2}+10 x y-y^{2}\) ?

Solution:-

ICSE Class 8 Maths Selina Solutions for Chapter 11-20

(ii) How much less \( 2 a^{2}+1 \text { is than } 3 a^{2}-6 \) ?

Solution:-

ICSE Class 8 Maths Selina Solutions for Chapter 11-21

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Concepts Learned in ICSE Class 8 Maths Chapter 11 – Algebraic Expressions

In this chapter students have studied the following new terms and concepts:

  1. Monomial: Expression that contains only one term is called a monomial.
  2. Binomial: Expression that contains two terms is called a binomial.
  3. Trinomial: An expression containing three terms is a trinomial.
  4. Polynomial: an expression containing one or more terms with non-zero coefficients (with variables having non-negative exponents) is called a polynomial.
  5. Definition of Degree and Coefficient along with the examples.
  6. Addition and subtraction of algebraic expressions.

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