How do you solve #x^2(a^2+2ab+b^2) = x(a+b)# by factoring?

1 Answer
Aug 21, 2015

Answer:

#x = 0" " # or #" "x = 1/(a+b)#

Explanation:

First, notice that you can write

#(a^2 + 2ab + b^2)#

as the square of #(a + b)#

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

Your equation can now be written as

#x^2 * (a+b)^2 = x * (a + b)#

You can simplify this equation by dividing both sides by #(a+b)#

#(x^2 * (a + b)^color(red)(cancel(color(black)(2))))/color(red)(cancel(color(black)((a+b)))) = (x * color(red)(cancel(color(black)((a+b)))))/color(red)(cancel(color(black)((a+b))))#

#x^2 * (a + b) = x#

Move all the terms to one side of the equation to get

#(a+b) * x^2 - x = 0#

#x * [(a+b)x - 1] = 0#

This equation will have two solutions, #x = color(green)(0)# and

#(a+b)x - 1= 0 implies x = color(green)(1/(a+b))#