RD Sharma Solutions Class 7 Algebraic Expressions Exercise 7.1

RD Sharma Class 7 Solutions Chapter 7 Ex 7.1 PDF Free Download

RD Sharma Solutions Class 7 Chapter 7 Exercise 7.1

Exercise 7.1

Q1) Identify the monomials, binomials, trinomials and quadrinomials from the following expressions:

(i) \(a{2}\)

(ii) \(a{2}-b{2}\)

(iii) \(x{3}+y{3}+z{3}\)

(iv)\(x{3}+y{3}+z{3}+3xyz\)

(v) 7 + 5

                                                       

(vi) abc + 1

(vii) 3x – 2 + 5

(viii) 2x – 3y + 4

(ix) xy + yz + zx

(x) \(ax{3}+bx{2}+cx+d\)

Solution:

The monomials, binomials, trinomials and quadrinomials are as follows.

(i) \(a{2}\) is a monomial expression as it contains one term only.

(ii) \(a{2}-b{2}\) is a binomial expression as it contains two terms.

(iii) \(x{3}+y{3}+z{3}\) is a trinomial expression as it contains three terms.

(iv) \(x{3}+y{3}+z{3}+3xyz\) is a quadrinomial expression as it contains four terms.

(v) 7 + 5 = 12 is a monomial expression as it contains one term only.

(vi) abc + 1 is a binomial expression as it contains two terms.

(vii) 3x – 2 + 5 = 3x + 3 is a binomial expression as it contains two terms.

(viii) 2x – 3y + 4 is a trinomial expression as it contains three terms.

(ix) xy + yz + zx is a trinomial expression as it contains three terms.

(x) \(ax{3}+bx{2}+cx+d\) is a quadrinomial expression as it contains four terms.

Q2) Write all the terms of each of the following algebraic expressions:

(i) 3x

(ii) 2x – 3

(iii) \(2x{2}-7\)

(iv) \(2x{2}+y{2}-3xy+4\)

Solution:

The terms of each of the given algebraic expressions are as follows.

(i) 3x is the onty term of the given algebraic expression.

(ii) 2x and -3 are the terms of the given algebraic expression.

(iii) \(2x{2}\;and\;-7\) are the terms of the given algebraic expression.

(iv) \(2x{2},\;y{2},\;-3xy\;and\;4\) are the terms of the given algebraic expression.

Q3) Identify the terms and also mention the numerical coefficients of those terms:

(i) \(4xy,\;-5x{2}y,\;-3yx,\;2xy{2}\)

(ii) \(7a{2}bc,\;-3ca{2}b,-\frac{5}{2}abc{2},\;\frac{3}{2}abc{2},\;-\frac{4}{3}cba{2}\)

Solution:

Like terms                                                      Numerical coefficients

(i)         4xy, -3yx                                                         4, -3

(ii)        {\(7a{2}bc,\;-3ca{2}b\)}           {7, -3}

{\(-\frac{5}{2}abc{2}\)}             {\(-\frac{5}{2}\)}

{\(\frac{3}{2}abc{2}\)}              {\(\frac{3}{2}\)}

{\(-\frac{4}{3}cba{2}\)}             {\(-\frac{4}{3}\)}

Q4) Identify the like terms in the following algebraic expressions:

(i) \(a{2}+b{2}-2a{2}+c{2}+4a\)

(ii) \(3x+4xy-2yz+\frac{5}{2}zy\)

(iii) \(abc+ab{2}c+2acb{2}+3c{2}ab+b{2}ac-2a{2}bc+3cab{2}\)

Solution:

The like terms in the given algebraic expressions are as follows.

(i) The like terms in the given algebraic expressions are \(a{2}\;and\;-2a{2}\).

(ii) The like terms in the given algebraic expressions are -2yz and \(\frac{5}{2}zy\).

(iii) The like terms in the given algebraic expressions are \(ab{2}c,\;2acb{2},\;b{2}ac\;and\;3cab{2}\).

Q5) Write the coefficient of x in the following:

(i) –12x            (ii) –7xy           (iii) xyz            (iv) –7ax

Solution:

The coefficients of x are as follows.

(i) The numerical coefficient of x is -12.

(ii) The numerical coefficient of x is -7y.

(iii) The numerical coefficient of x is yz.

(iv) The numerical coefficient of x is -7a.

 Q6) Write the coefficient of \({2}\) in the following:

(i) \(-3x{2}\)

(ii) \(5x{2}yz\)

(iii) \(\frac{5}{7}x{2}z\)

(iv) \(-\frac{3}{2}ax{2}+yx\)

Solution:

The coefficient of \(x{2}\) are as follows.

(i) The numerical coefficient of \(x{2}\) is -3.

(ii) The numerical coefficient of \(x{2}\) is 5yz.

(iii) The numerical coefficient of \(x{2}\) is \(\frac{5}{7}z\).

(iv) The numerical coefficient of \(x{2}\) is \(-\frac{3}{2}a\).

Q7) Write the coefficient of:

(i) y in –3y

(ii) a in 2ab

(iii) z in –7xyz

(iv) p in –3pqr

(v) \(y{2}\;in\;9xy{2}z\)

(vi) \(x{3}\;in\;x{3}+1\)

(vii) \(x{2}\;in\;-x{2}\)

Solution:

The coefficients are as follows.

(i) The coefficient of y is -3.

(ii) The coefficient of a is 2b.

(iii) The coefficient of z is -7xy.

(iv) The coefficient of p is -3qr.

(v) The coefficient of \(y{2}\) is 9xz.

(vi) The coefficient of \(x{3}\) is 1.

(vii) The coefficient of \(-x{2}\) is -1.

Q8) Write the numerical coefficient of each in the following

(i) xy

(ii) -6yz

(iii) 7abc

(iv) \(-2x{3}y{2}z\)

Solution:

The numerical coefficient of each of the given terms is as follows.

(i) The numerical coefficient in the term xy is 1.

(ii) The numerical coefficient in the term -6yz is -6.

(iii) The numerical coefficient in the term 7abc is 7.

(iv) The numerical coefficient in the term \(-2x{3}y{2}z\) is -2.

Q9) Write the numerical coefficient of each term in the following algebraic expressions:

(i) \(4x{2}y-\frac{3}{2}xy+\frac{5}{2}xy{2}\)

(ii) \(-\frac{5}{3}x{2}y+\frac{7}{4}xyz+3\)

Solution:

The numerical coefficient of each term in the given algebraic expression is as follows.

Term Coefficient
(i)

\(4x{2}y\)

\(-\frac{3}{2}xy\)

\(\frac{5}{2}xy{2}\)

4

\(-\frac{3}{2}\)

\(\frac{5}{2}\)

(ii)

\(-\frac{5}{3}x{2}y\)

\(\frac{7}{4}xyz\)

3

\(-\frac{5}{3}\)

\(\frac{7}{4}\)

3

Q10) Write the constant term of each of the following algebraic expressions:

(i) \(x{2}y-xy{2}+7xy-3\)

(ii) \(a{3}-3a{2}+7a+5\)

Solution:

The constant term of each of the given algebraic expressions is as follows.

(i) The constant term in the given algebraic expressions is -3.

(ii) The constant term in the given algebraic expressions is 5.

Q11) Evaluate each of the following expressions for x = -2, y = -1, z = 3:

(i) \(\frac{x}{y}+\frac{y}{z}+\frac{z}{x}\)

(ii) \(x

{2}+y

{2}+z

{2}-xy-yz-zx\)\(\frac{x}{y}+\frac{y}{z}+\frac{z}{x}=\frac{-2}{-1}+\frac{-1}{3}+\frac{3}{-2}=\frac{12-2-9}{6}=\frac{1}{6}\)

(ii) \(x{2}+y{2}+z{2}-xy-yz-zx\)

= \((-2){2}+(-1){2}+(3){2}-(-2)(-1)-(-1)(3)-(3)(-2)\)

= 4 + 1 + 9 – 2 + 3 + 6

= (4 + 1 + 9 + 3 + 6) – 2

= 23 – 2

= 21

Q12) Evaluate each of the following algebraic expressions for x = 1, y = -1, z = 2, a = -2, b = 1, c = -2:

(i) ax + by + cz

(ii) \(ax{2}+by{2}-cz

{2}\)

(iii) axy + byz + cxy

Solution:

We have x = 1, y = -1, z = 2, a = -2, b = 1 and c = -2.

Thus,

(i) ax + by + cz

= (-2)(1) + (1)(-1) + (-2)(2)

= –2 – 1 – 4

= –7

(ii)  \(ax{2}+by{2}-cz

{2}\)\((-2)(1){2}+(1)(-1)

{2}-(-2)(2)

{2}\) -->

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