Question

FACTORISATION 1) x2-4. 2)a8-36 3)x2y2-a2. 4)1-4c12. 5)a2-2+1/a2.

Answer 1

$\boxed{\boxed{\boxed{\bold{\pink{Solution : \longrightarrow}}}}}$

$\bold\blue{1) \: {x}^{2} - 4} \\ \\ \bold\blue{= (x) {}^{2} - (2) {}^{2}} \\ \\ \bold\blue{= (x + 2)(x - 2)}$

$\bold\red{2) \: {a}^{8} - 36} \\ \\ \bold\red{= ({a}^{4} ) {}^{2} - (6) {}^{2}} \\ \\ \bold\red{= ( {a}^{4} + 6)( {a}^{4} - 6)}$

$\bold\purple{3) \: {x}^{2} {y}^{2} - {a}^{2}} \\ \\ \bold\purple{= {(xy)}^{2} - {(a)}^{2}} \\ \\ \bold\purple{= (xy + a)(xy - a)}$

$\bold\green{4) \: 1 - 4 {c}^{12}} \\ \\ \bold\green{= (1) {}^{2} - (2 {c}^{6} ) {}^{2}} \\ \\ \bold\green{= (1 + 2 {c}^{6} )(1 - 2 {c}^{6} )}$

$\bold{5) \: {a}^{2} - 2 + \frac{1}{ {a}^{2} } }\\ \\ \bold{= (a) {}^{2} - 2.a. \frac{1}{a} + ( \frac{1}{a} ) {}^{2} }\\ \\ \bold{= (a - \frac{1}{a} ) {}^{2} }\\ \\ \bold{= (a - \frac{1}{a} )(a - \frac{1}{a} )}$

$\boxed{\boxed{\boxed{\bold{\green{Have \: \: a \: \: nice \: \: day.}}}}}$