Algebraic Expressions And Identities : Exercise 9.2 (Mathematics NCERT Class 8th)

Q.1 Find the product of the following pairs of monomials.

(i) 4, 7p (ii) – 4p, 7p (iii) – 4p, 7pq (iv) 4, – 3p

(v) 4p, 0

Sol. The product of given pair of monomials are as follows:

(i) $4 \times 7p = 4 \times 7 \times p = 28p$

(ii) $- 4p \times 7p = - 4 \times p \times 7 \times p = ( - 4 \times 7) \times (p \times p) = - 28{p^2}$

(iii) $- 4p \times 7pq = - 4 \times p \times 7 \times p \times q = ( - 4 \times 7) \times (p \times p \times q) = - 28{p^2}q$

(iv) $4{p^3} \times - 3p = 4 \times ( - 3) \times p \times p \times p \times p = - 12{p^4}$

(v) $4p \times 0 = 4 \times p \times 0 = 0$

Q.2 Find the areas of rectangles with the following pairs of monomials as their lengths and breadths respectively.

$(p,q);(10m,5n);(20{x^2},5{y^2});(4x,3{x^2});(3mn,4np)$

Sol. We know that, area of rectangle = length x breadth

For$(p,q)$: area = $p \times q = pq$

For$(10m,5n)$: area = $10m \times 5n = 10 \times 5 \times m \times n = 50mn$

For$(20{x^2},5{y^2})$: area = $20{x^2} \times 5{y^2} = 20 \times 5 \times {x^2} \times {y^2} = 100{x^2}{y^2}$

For$(4x,3{x^2})$: area = $4x \times 3{x^2} = 4 \times 3 \times x \times {x^2} = 12{x^3}$

For$(3mn,4np)$: area = $3mn \times 4np = 3 \times 4 \times m \times n \times n \times p = 12m{n^2}p$

Q.3 Complete the table of products.

Sol. The complete table is as shown below:

Q.4 Obtain the volume of rectangular boxes with the following length, breadth and height respectively.

(i) $5a,3{a^2},7{a^4}$ (ii) $2p,4q,8r$ (iii) $xy,2{x^2}y,2x{y^2}$ (iv) $a,2b,3c$

Sol. We know that, volume of rectangle = length x breadth x height

(i) $5a,3{a^2},7{a^4}$

Volume = $5a \times 3{a^2} \times 7{a^4} = 5 \times 3 \times 7 \times a \times {a^2} \times {a^4} = 105{a^7}$

(ii) $2p,4q,8r$

Volume = $2p \times 4q \times 8r = 2 \times 4 \times 8 \times p \times q \times r = 64pqr$

(iii) $xy,2{x^2}y,2x{y^2}$

Volume = $xy \times 2{x^2}y \times 2x{y^2} = 2 \times 2 \times xy \times {x^2}y \times x{y^2} = 4{x^4}{y^4}$

(iv) $a,2b,3c$

Volume = $a \times 2b \times 3c = 2 \times 3 \times a \times b \times c = 6abc$

Q.5 Obtain the product of

(i) $xy,yz,zx$ (ii) $a, - {a^2},{a^3}$ (iii) $2,4y,8{y^2},16{y^3}$

(iv) $a,2b,3c,6abc$ (v) $m, - mn,mnp$

Sol. The product are as follows:

(i) $xy,yz,zx$

$xy \times yz \times zx = {x^2}{y^2}{z^2}$

(ii) $a, - {a^2},{a^3}$

$a \times ( - {a^2}) \times {a^3} = - {a^6}$

(iii) $2,4y,8{y^2},16{y^3}$

$2 \times 4y \times 8{y^2} \times 16{y^3} = 2 \times 4 \times 8 \times 16 \times y \times {y^2} \times {y^3} = 1024{y^6}$

(iv) $a,2b,3c,6abc$

$a \times 2b \times 3c \times 6abc = 2 \times 3 \times 6 \times a \times b \times c \times abc$

(v) $m, - mn,mnp$

$m \times ( - mn) \times mnp = - {m^3}{n^2}p$