Factorise:
(i) $25 - 4 x^{2} - 12 x y - 9 y^{2}$
(ii) $x^{2} - a^{2} + 10 a b - 25 b^{2}$
(iii) $6 x y + x^{2} + 9 y^{2} - 4 a^{2}$
(iv) $9 x^{2} + 4 + 12 x - a^{2} + 2 a b - b^{2}$

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Solution

i) $25 - 4 x^{2} - 12 x y - 9 y^{2}$
$= 25 - (4 x^{2} + 12 x y + 9 y^{2})$
$= 5^{2} - ({(2 x)}^{2} + 2 \times 2 x \times 3 y + {(3 y)}^{2})$
$= 5^{2} - (2 x + 3 y)^{2}$
$= (5 + 2 x + 3 y) (5 - (2 x + 3 y))$
$= (5 + 2 x + 3 y) (5 - 2 x - 3 y)$

ii) $x^{2} - a^{2} + 10 a b - 25 b^{2}$
$= x^{2} - (a^{2} - 10 a b + 25 b^{2})$
$= x^{2} - (a^{2} - 2 \times a \times 5 b + (5 b)^{2})$
$= x^{2} - (a - 5 b)^{2}$
$= (x + a - 5 b) (x - (a - 5 b))$
$= (x + a - 5 b) (x - a + 5 b)$

iii) $6 x y + x^{2} + 9 y^{2} - 4 a^{2}$
$= (2 \times x \times 3 y + x^{2} + (3 y)^{2}) - (2 a)^{2}$
$= (x + 3 y)^{2} - (2 a)^{2}$
$= (x + 3 y + 2 a) (x + 3 y - 2 a)$

iv) $9 x^{2} + 4 + 12 x - a^{2} + 2 a b - b^{2}$
$= ((3 x)^{2} + (2^{2}) + 2 \times 3 x \times 2) - (a^{2} - 2 a b + b^{2})$
$= (3 x + 2)^{2} - (a - b)^{2}$
$= (3 x + 2 + a - b) (3 x + 2 - (a - b))$
$= (3 x + 2 + a - b) (3 x + 2 - a + b)$

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Similar questions

Q. Factorise:
(i)

4 x^{2} + 9 y^{2} + 16 z^{2} + 12 x y - 24 y z - 16 x z

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a^{2} + 6 b x - 9 b^{2} x^{2} - 10 a b - 1 + 25 b^{2}

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(i) x² + 14x + 49; (ii) 4x² + 4x + 1; (iii) a² − 10a + 25; (iv) 2x² − 24x + 72;

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(i) $4 a^{2} - 25$ (ii) $x^{2} - \frac{9}{16}$ (iii) $x^{4} - y^{4}$ (iv) $[7 \frac{3}{10}]^{2} - [2 \frac{1}{10}]^{2}$ (v) $(0.7)^{2} - (0.3)^{2}$ (vi) $(5 a - 2 b)^{2} - (2 a - b)^{2}$

Factorise:

(i) x² + 6x + 8; (ii) x² + 4x + 3; (iii) a² + 5a + 6; (iv) a² − 5a + 6; (v) a² − 3a − 40; (vi) x² − x − 72.

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Factorise:(i)25−4x2−12xy−9y2(ii)x2−a2+10ab−25b2(iii)6xy+x2+9y2−4a2(iv)9x2+4+12x−a2+2ab−b2

Factorise:
(i) $25 - 4 x^{2} - 12 x y - 9 y^{2}$
(ii) $x^{2} - a^{2} + 10 a b - 25 b^{2}$
(iii) $6 x y + x^{2} + 9 y^{2} - 4 a^{2}$
(iv) $9 x^{2} + 4 + 12 x - a^{2} + 2 a b - b^{2}$