Question

Factorise : (a² - a) (4a² - 4a - 5) - 6

Answer 1

Let us assume, a² - a = x
Then the given expression is,
(a² - a) (4a² - 4a - 5) - 6
= x( 4x - 5 ) - 6
= 4x² - 5x - 6
= 4x² - 8x + 3x - 6
= 4x( x - 2 ) + 3( x - 2 )
= ( 4x + 3 )( x - 2 )
= [ 4( a² - a ) + 3 ]( a² - a - 2 )          [ resubstitute the value of x ]
= [ 4a² - 4a + 3 ]( a² - a - 2 )
= [ 4a² - 4a + 3 ]( a² - 2a + a - 2 )
= [ 4a² - 4a + 3 ][ a( a - 2 ) + 1( a - 2 )]
= [ 4a² - 4a + 3 ]( a - 2 )( a + 1 )