Question

$(x + 2y) ^{2} - 4(2x - y) ^{2} \\ factorise \: the \: above$
with steps.....

Answer 1

Given (x+2y)^2 - 4(2x - y)^2

It is in the form of x^2 - y^2 = (x+y)(x-y).

= (2(2x-y)+(x+2y))(x+2y)-2(2x-y) can be written as

= (x + 2y + 2(2x - y)) (x + 2y - 2(2x-y))

= (x + 2y + 4x - 2y) (x + 2y - 4x + 2y)

= (5x)(-3x + 4y)

(or)

5x(4y - 3x).


Hope this helps!