Factorise:
(i) $a x + b x + a y + b y$
(ii) $a x^{2} + b y^{2} + b x^{2} + a y^{2}$
(iii) $a^{2} + b c + a b + a c$
(iv) $a x - a y + b x - b y$

Open in App

Solution

(i) $a x + b x + a y + b y = (a x + b x) + (a y + b y)$ [Grouping the terms]
$= (a + b) x + (a + b) y$
$= (a + b) (x + y)$ [Taking (a+b) common]
(ii) $a x^{2} + b y^{2} + b x^{2} + a y^{2} = a x^{2} + b x^{2} + a y^{2} + b y^{2}$ [Re-arranging the terms]
$= (a + b) x^{2} + (a + b) y^{2} = (a + b) (x^{2} + y^{2})$ [Takin (a+b) common]
(iii) $a^{2} + b c + a b + a c = (a^{2} + a b) + (a c + b c)$ [Re-grouping the terms]
$= a (a + b) + (a + b) c = (a + b) (a + c)$ [Taking (a+b) common]
(iv) $a x - a y + b y - b y = a (x - y) + b (x - y)$
$= (a + b) (x - y)$ [Taking (x-y) common]

Suggest Corrections

Similar questions

(i) a x + b x + a y + b y

(i i) a x^{2} + b y^{2} + b x^{2} + a y^{2}

(i i i) a^{2} + b c + a b + a c

(i v) a x - a y + b x - b y

Factorise : $x y - a y - a x + a^{2} + b x - a b$

a x + b x - a y - b y

x

y

a x + b y = 1

b x + a y = \frac{(a + b)^{2}}{a^{2} + b^{2}} - 1

b x + a y = \frac{2 a b}{a^{2} + b^{2}}

Join BYJU'S Learning Program