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

Question

7769 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-11-15T22:41:52

$49x^2+64y^2 = (7x-8iy)(7x+8iy)$

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:

$a^2-b^2 = (a-b)(a+b)$

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

$49x^2 + 64y^2 = (7x)^2 + (8y)^2 = (7x)^2 - (8iy)^2$

$= (7x-8iy)(7x+8iy)$

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