Question

Factorise : 5 - (3a² - 2a) (6 - 3a² + 2a)

Answer 1

5 - (3a² - 2a) (6 - 3a² + 2a)
= 5 - ( 3a² - 2a )[ 6 - ( 3a² - 2a )]
Assume that 3a² - 2a = x
Therefore,
5 - ( 3a² - 2a )( 6 - 3a² + 2a )
= 5 - x( 6 - x )
= 5 - 6x + x²
= 5( 1 - x ) - x( 1 - x )
= ( 5 - x )( 1 - x )
= ( x - 5 )( x - 1 )
= ( 3a² - 2a - 5 )( 3a² - 2a - 1 )
= ( 3a² - 5a + 3a -5 )(3a² - 3a + a - 1 )
= [ a( 3a - 5 ) + 1( 3a - 5)][3a( a - 1) + 1( a - 1)]
= ( 3a - 5 )( a + 1 )( 3a + 1 )( a - 1 )