How do you factor the expression #(2x-3)^3 (x+1) +(x-3) (2x-3)^2#?
1 Answer
Jan 12, 2016
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
#(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))#
