# How do you factor 49x^2 + 64y^2 ?

Nov 15, 2015

$49 {x}^{2} + 64 {y}^{2} = \left(7 x - 8 i y\right) \left(7 x + 8 i y\right)$

#### Explanation:

This quadratic has no linear factors with Real coefficients, but it can be treated as a difference of squares using pure imaginary coefficients,

The difference of squares identity can be written:

${a}^{2} - {b}^{2} = \left(a - b\right) \left(a + b\right)$

Use this with $a = 7 x$ and $b = 8 i y$ as follows:

$49 {x}^{2} + 64 {y}^{2} = {\left(7 x\right)}^{2} + {\left(8 y\right)}^{2} = {\left(7 x\right)}^{2} - {\left(8 i y\right)}^{2}$

$= \left(7 x - 8 i y\right) \left(7 x + 8 i y\right)$