Question

Factorise:
(i) x^2 + xy + 8x + 8y
(ii) 15xy – 6x + 5y – 2
(iii) ax + bx – ay – by
(iv) 15pq + 15 + 9q + 25p
(v) z – 7 + 7xy – xyz​

Answer 1

${\huge{\sf\green{\underline{\underline{\blue{ Solution:-}}}}}}$

$(i) x² + xy + 8x + 8y$

Grouping the terms, we have

$x² + xy + 8x + 8y$

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

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

Hence, the required factors $= (x + y)(x + 8)$

(ii) $15xy – 6x + 5y – 2$

Grouping the terms, we have

$(15xy – 6x) + (5y – 2)$

$= 3x(5y – 2) + (5y – 2)$

$= (5y – 2)(3x + 1)$

(iii) $ax + bx – ay –by$

Grouping the terms, we have

$= (ax – ay) + (bx – by)$

$= a(x – y) + b(x – y)$

$= (x – y)(a + b)$

Hence, the required factors $= (x – y)(a + b)$

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

Grouping the terms, we have

$= (15pq + 25p) + (9q + 15)$

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

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

Hence, the required factors $= (3q + 5) (5p + 3)$

(v)$z – 7 + 7xy – xyz$

Grouping the terms, we have

$= (-xyz + 7xy) + (z – 7)$

$= -xy(z – 7) + 1 (z – 7)$

$= (-xy + 1) (z – 1)$

Hence the required factor $= -(1 – xy) (z – 7)$