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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.

First monomial →__

Second monomial↓

2x  - 5y 3{x^2}  - 4xy 7{x^2}y  - 9{x^2}{y^2}
2x 4{x^2} ... ... ... ... ...
 - 5y ... ...  - 15{x^2}{y^2} ... ... ...
3{x^2} ... ... ... ... ... ...
 - 4xy ... ... ... ... ... ...
7{x^2}y ... ... ... ... ... ...
 - 9{x^2}{y^2} ... ... ... ... ... ...

Sol. The complete table is as shown below:

First monomial →__

Second monomial↓

2x  - 5y 3{x^2}  - 4xy 7{x^2}y  - 9{x^2}{y^2}
2x 4{x^2}  - 10xy 6{x^3}  - 8{x^2}y 14{x^3}y  - 18{x^3}{y^2}
 - 5y  - 10xy 25{y^2}  - 15{x^2}{y^2} 20x{y^2}  - 35{x^2}{y^2} 45{x^2}{y^3}
3{x^2} 6{x^3}  - 15{x^2}y 9{x^4}  - 12{x^3}y 21{x^4}y  - 27{x^4}{y^2}
 - 4xy  - 8{x^2}y 20x{y^2}  - 12{x^3}y 16{x^2}{y^2}  - 28{x^3}{y^3} 36{x^3}{y^3}
7{x^2}y 14{x^3}y  - 35{x^2}{y^2} 21{x^4}y  - 28{x^3}{y^3} 49{x^4}{y^2}  - 63{x^4}{y^3}
 - 9{x^2}{y^2}  - 18{x^3}{y^2} 45{x^2}{y^3}  - 27{x^4}{y^2} 36{x^3}{y^3}  - 63{x^4}{y^3} 81{x^4}{y^4}

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

 



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