Exercise 11.2

1. Complete the table:

S.No.	First Expression	Second Expression	Product
1	5q	p+q-2r	5q(p+q-2r) = 5pq+5q2-10qr
2	kl+lm+mn	3k
3	ab2	a+b2+c3
4	x-2y+3z	xyz
5	a2bc+b2cd−abd2	a2b2c2

Solution:

S.No.	First Expression	Second Expression	Product
1	5q	p+q-2r	5q(p+q-2r) = 5pq+5q2-10qr
2	kl+lm+mn	3k	3k(kl+lm+mn) = + +
3	ab2	a+b2+c3	ab2a+b2+c3 = + +
4	x-2y+3z	xyz	xyz(x-2y+3z) = - +
5	a2bc+b2cd−abd2	a2b2c2	a2b2c2a2bc+b2cd−abd2 = + -

2. Simplify: 4y(3y+4)

Solution:

4y(3y + 4) = 4y × 3y + 4y × 4 = +

3. Simplify x(2x2-7x+3) and find the values of it for (i) x = 1 and (ii) x = 0

Solution:

x(2x2-7x+3) = - +

(i) For x = 1: 213 - 712 + 3(1) = - + =

(ii) For x = 0: 203 - 702 + 3(0) =

4. Add the product: a(a-b), b(b-c), c(c-a)

Solution:

a(a - b) + b(b - c) + c(c - a) = - + - + - .

5. Add the product: x(x+y-r), y(x-y+r), z(x-y-z)

Solution:

x(x + y - r) + y(x - y + r) + z(x - y - z) = + - + - + + - - (Enter answers in order)

6. Subtract the product of 2x(5x-y) from product of 3x(x+2y)

Solution:

3x(x + 2y) - 2x(5x - y) = 3x2+6xy - 10x2−2xy = 3x2 + 6xy - 10x2 + 2xy = + .

7. Subtract 3k(5k-l+3m) from 6k(2k+3l-2m)

Solution:

6k(2k + 3l - 2m) - 3k(5k - l + 3m) = ( k2 + kl - km) - ( k2 - kl + km)

= 12k2 + 18kl - 12km - 15k2 + 3kl - 9km

= k2 + kl - km.

8. Simplify: a2(a-b+c)+a2(a+b-c)-c²(a-b-c)

Solution:

a2a−b+c + b2a+b−c - c2a−b−c = - + + + - - + +

= + + - + + - - +

Chapter 11: Algebraic Expressions