# RD Sharma Solutions Class 7 Algebraic Expressions Exercise 7.1

## RD Sharma Solutions Class 7 Chapter 7 Exercise 7.1

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

#### 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}$ -->

#### Practise This Question

Find the height of the cylinder whose capacity is 1540 L and diameter of the base is 140 cm?