How do you factor completely  6x^2 + 18xy + 12y^2?

Jun 21, 2016

$6 \left(x + 2 y\right) \left(x + y\right)$

Explanation:

Always look to see if there is a common factor first.
In this case you can divide out a factor of 6 from all the terms.

$6 \left({x}^{2} + 3 x y + 2 {y}^{2}\right)$

Now, the factors of 2 which add up to 3 are 2 and 1.
The signs are the same, they are both positive.
There will be an x and a y term in each bracket.

$6 \left(x + 2 y\right) \left(x + y\right)$