Question

Factorize 4(x-y) ² – 12(x – y)(x + y) + 9(x + y)²
$\left[4Marks\right]$

Answer 1

Consider ( x – y ) = p, ( x + y ) = q

= 4p² – 12pq + 9q²

Expanding the middle term, -12 = -6 -6 also 4× 9=-6 × -6

= 4p² – 6pq – 6pq + 9q²
$\left[1Mark\right]$

=2p( 2p – 3q ) -3q( 2p – 3q )

= ( 2p – 3q ) ( 2p – 3q )

= ( 2p – 3q )²
$\left[1Mark\right]$

Substituting back p = x – y and q = x + y;

= [2( x-y ) – 3( x+y)]² = [ 2x – 2y – 3x – 3y ] ²

= (2x-3x-2y-3y ) ²

=[ -x – 5y] ²
$\left[1Mark\right]$

=[( -1 )( x+5y )] ²

=( x+5y ) ²

Therefore, 4(x-y) ² – 12(x – y)(x + y) + 9(x + y)² = ( x+5y )²
$\left[1Mark\right]$