Factorize: (i) x²+ 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) x² + 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

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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) x²+ 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)

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