How do you factor the expression #(2x-3)^3 (x+1) +(x-3) (2x-3)^2#?

1 Answer
Jan 12, 2016

Answer:

Combine, simplify and use the difference of squares identity to find:

#(2x-3)^3(x+1)+(x-3)(2x-3)^2#

#=2(2x-3)^2(x-sqrt(3))(x+sqrt(3))#

Explanation:

The difference of squares identity can be written:

#a^2-b^2=(a-b)(a+b)#

We use this with #a=x# and #b=sqrt(3)# below...

#(2x-3)^3(x+1)+(x-3)(2x-3)^2#

#=(2x-3)^2((2x-3)(x+1)+(x-3))#

#=(2x-3)^2((2x^2-x-3)+(x-3))#

#=(2x-3)^2(2x^2-6)#

#=2(2x-3)^2(x^2-3)#

#=2(2x-3)^2(x^2-(sqrt(3))^2)#

#=2(2x-3)^2(x-sqrt(3))(x+sqrt(3))#