Factorize:- (i) $25 x^{2} - y^{2}$
(ii) $4 - 25 x^{2}$
(iii) $(x + y)^{2} - 1$

Open in App

Solution

(i) $25 x^{2} - y^{2}$
$= (5 x)^{2} - y^{2}$ $[∵ a^{2} - b^{2} = (a - b) (a + b)]$
$(5 x - y) (5 x + y)$
(ii) $4 - 25 x^{2}$
$= (2)^{2} - (5 x)^{2}$ $[∵ a^{2} - b^{2} = (a - b) (a + b)]$
$= (2 - 5 x) (2 + 5 x)$
(iii) $(x + y)^{2} - 1$ $[∵ (a + b)^{2} = a^{2} + b^{2} + 2 a b, a^{2} - b^{2} = (a - b) (a + b)]$
$= (x + y)^{2} - (1)^{2}$
$= (x + y - 1) (x + y + 1)$

Suggest Corrections

Similar questions

\frac{25 x^{2}}{4} - \frac{y^{2}}{9}

{(\sqrt{5} + \sqrt{2})}^{2}

The locus of a point which divides the join of A(-1, 1) and a variable point P on the circle $x^{2} + y^{2} = 4$ in the ratio 3:2, is

25 (x^{2} + y^{2} - 2 x + 1) = (4 x - 3 y + 1)^{2}

Factorize the following :

$i .) 25 x^{2} - 36$

$i i .) 36 x^{2} + 49 + 8 x$

$i i i .) 9 + 25 x^{2} - 30 x$ [3 MARKS]

P A

P B

x^{2} + y^{2} = 9

P

x + y = 25,

A B

Join BYJU'S Learning Program