Question

factorise
$125 - 8a^3 - 27b^3 - 90ab$

Answer 1

Heya frnd...

Uing idenity - a3 + b3 + c3 - 3abc = ( a + b + c ) ( a2 + b2 + c2 - ab - bc - ca )

125 - 8a3 - 27b3 - 90ab

(5)3 - (2a)3 - (3b)3 - 3 . 5 . 2a . 3b

[ 5 (-2a) + (-3b) ] [ (5)2 + (-2a)2 + (-3b)2 - (5 . -2a) - ( -2a . -3b ) - ( -3c . 5 )

( 5 - 2a - 3b ) ( 25 + 4a2 + 9b2 + 10a - 6ab + 15c )

Hope it helps

Answer 2

Use the identity :-

a³ + b³ + c³ - 3abc = ( a + b + c )³

==> ( a² + b² + c² - ab - bc - ca )

125 - 8a³ - 27b³ - 90ab

(5)³ - (2a)³ - (3b)³ - 3.5.2a.3b

[ 5(-2a)³ + (-3b) ] [ 5² + (-2a)² + (-3b)² - (5.-2a) - (-2a.-3b) - ( -3c.5) ]

( 5 - 2a - 3b ) ( 25 + 4a² + 9b² + 10a - 6ab + 15c )