# Factorize: (i) x^{2}+ xy + 8x + 8 y (ii) 15xy- 6x + 5 y - 2

(iii) ax + bx - ay - by (iv) 15 pq +15 + 9q + 25 p

(v) z - 7 + 7xy - xyz

**Solution:**

Factorization is a method of finding factors for any mathematical object, be it a number, a polynomial or any algebraic expression. Thus, factorization of an algebraic expression refers to finding out the factors of the given algebraic expression.

There are 4 terms in each expression. First, we will make pair of two terms from which we can take out common factors and convert the expression of 4 terms into 2 terms expression followed by taking out common factors from the remaining 2 terms.

(i) x^{2} + xy + 8x + 8y

= x × x + x × y + 8 × x + 8 × y

= x(x + y) + 8(x + y)

= (x + y) (x + 8)

(ii) 15xy - 6x + 5y - 2

= 3 × 5 × x × y - 3 × 2 × x + 5 × y - 2

= 3x (5y - 2) + 1(5y - 2)

= (5y - 2) (3x + 1)

(iii) ax + bx - ay - by = a × x + b × x - a × y - b × y

= x(a + b) - y(a + b)

= (a + b)(x - y)

(iv) 15pq + 15 + 9q + 25 p

= 15pq + 9q + 25p + 15

= 3 × 5 × p × q + 3 × 3 × q + 5 × 5 × p + 3 × 5

= 3q(5p + 3) + 5(5p + 3)

= (5p + 3)(3q + 5)

(v) z - 7 + 7xy - xyz

= z - xyz - 7 + 7xy

= z - x × y × z - 7 + 7 × x × y

= z(1- xy) - 7(1 - xy)

= (1 - xy)(z - 7)

**☛ Check: **NCERT Solutions for Class 8 Maths Chapter 14

**Video Solution:**

## Factorize: (i) x²+ xy + 8x + 8y (ii) 15xy- 6x + 5 y - 2 (iii) ax+ bx - ay - by (iv) 15 pq +15 + 9q + 25 p (v) z - 7 + 7xy - xyz

Class 8 Maths NCERT Solutions Chapter 14 Exercise 14.1 Question 3

**Summary:**

The following expressions: (i) x^{2}+ xy + 8x + 8 y (ii) 15xy- 6x + 5 y - 2 (iii) ax+ bx - ay - by (iv) 15 pq +15 + 9q + 25 p (v) z - 7 + 7xy - xyz are factorised as (i) (x + y) (x + 8) (ii) (5y - 2) (3x + 1) (iii) (a + b) (x - y) (iv) (5p + 3) (3q + 5) (v) (1 - xy) (z - 7)

**☛ Related Questions:**

- Find the common factors of the terms (i) 12x, 36 (ii)2y, 22xy (iii)14pq, 28p2q2 (iv)2x, 3x2, 4 (v) 6abc, 24ab2, 12a2b (vi) 16x3, - 4x2, 32x (vii)10 pq, 20qr, 30rp (viii)3x2 y3, 10x3y2, 6x2y2z
- Factorise the following expressions (i) 7x - 42 (ii) 6p-12q (iii) 7a2+14a (iv) -16z + 20z3 (v) 20l2m + 30alm (vi) 5x2y -15xy2 (vii) 10a2 -15b2 + 20c2 (viii) -4a2 + 4ab - 4ca (ix) x2yz + xy2z + xyz2 (x) ax2y + bxy2 + cxyz
- Factorize the following expressions. (i) a2 + 8a +16 (ii) p2 -10 p + 25 (iii) 25m2 + 30m + 9 (iv) 49 y2 + 84 yz + 36z2 (v) 4x2 - 8x + 4 (vi) 121b2 - 88bc +16c2 (vii) (l +m)2 - 4lm (Hint: Expand (l + m)2 first) (viii) a4+ 2a2b2 + b4.
- Factorize (i) 4 p2 - 9q2 (ii) 63a2 - 112b2 (iii) 49x2 - 36 (iv) 16x5 - 144x3 (v) (l + m)2 - (l - m)2 (vi) 9x2y2 - 16 (vii) (x2 - 2xy + y2) - z2 (viii) 25a2 - 4b2 + 28bc - 49c2

visual curriculum