Question

help me to factor this:
x^2-27x^2a^3

Answer 1

You can factorize by x^2:
x^2*(1 - 27a^3)
The difference within brackets is a difference of cubes:
a^3 - b^3 = (a-b)(a^2 + ab + b^2)
Let a = 1 and b = 3a
1 - 27a^3 = (1-3a)(1 + 3a + 9a^2)
The factors are:
x^2*(1 - 3a)(1 + 3a + 9a^2)

Answer 2

First you want to factor out anything you see in common between the two terms. Looks like there is an x^2 in common:

\[x^2-27x^2a^3 \Rightarrow x^2(1-27a^3)\]
Then, you should notice something about that last term:
\[1-27a^3 \Rightarrow 1^3-(3a)^3\]
That is a difference of 2 cubes, which follows this formula:
\[x^3-y^3 = (x-y)(x^2+xy+y^2)\]
so we have:
\[1^3-(3a)^3 = (1-3a)(1+3a+9a^2)\]
So the final answer is:
\[x^2(1-3a)(1+3a+9a^2)\]