How do you factor #2(x - 2y)^2- 4x(x - 2y)#?

1 Answer
Sep 26, 2015

Answer:

#2(x - 2y)^2- 4x(x - 2y)= color(green)(-2(x-2y)(x+2y)#

Explanation:

#2(x - 2y)^2- 4x(x - 2y)#

In the given expression, we can see that the Binomial #x-2y# and the number 2 are common to both the terms. Taking this common factor out, we get:

#2(x-2y){(x-2y) - 2x}#

# = 2(x-2y){x - 2y - 2x}#

# = 2(x-2y){(x-2x) - 2y}#

# = 2(x-2y){-x-2y}#

# = 2(x-2y){-(x+2y)}#

# = color(green)(-2(x-2y)(x+2y)#

This is the completely factorised form of the given expression