Question

factorise: a^6 - b^6

Answer 1

Solution

$a {}^{6} - b {}^{6} \\ =( a {}^{3} ) {}^{2} - (b {}^{3} ) {}^{2} \\ = (a {}^{3} - b {}^{3} )(a {}^{3} + b {}^{3} ) \\ = (a - b)(a {}^{2} + b {}^{2} + ab)(a + b)(a {}^{2} + b {}^{2} - ab) \\ = (a + b)(a - b)(a {}^{2} + b {}^{2} + ab)(a {}^{2} + b {}^{2} - ab)$

Thank....u....

Answer 2

a⁶-b⁶

= (a²)³ - (b²)³

= (a²-b²) [(a²)²+2a²b²+(b²)²]

= (a-b) (a+b) (a⁴+a²b²+b⁴)

= (a-b) (a+b) [{(a²)²+2a²b²+(b²)²}-a²b²]

= (a-b) (a+b) (a²+b²+ab) (a²+b²-ab)

= (a-b) (a+b) (a²+ab+b²) (a²-ab+b²)