# How do you factor 4x^2 + 5xy + 16x + 20y?

May 23, 2015

4-term polynomials like this need to be factored first as two binomials.

$4 {x}^{2} + 5 x y + 16 x + 20 y$

$\left(4 {x}^{2} + 5 x y\right) + \left(16 x + 20 y\right)$

'X' can be factored from the left side and 4 can be factored from the right side.

$x \left(4 x + 5 y\right) + 4 \left(4 x + 5 y\right)$

According to the converse of the distributive property, I can combine these two terms.

$\left(x + 4\right) \left(4 x + 5 y\right)$