Question

How do you factor completely `45x^4 + 43x^2 y^2 - 28y^4`?

Answer 1

`(3x+2y)(3x-2y)(5x^2+7y^2)`

Explanation:

Given
`color(white)("XXX")45x^4+43x^2y^2-28y^4`

Replacing `p=x^2` and `q=y^2`
`color(white)("XXX")=45p^2+43pq-28q^2`

Factoring by examining factors of `45` and `28`
or by using the quadratic formula:
`color(white)("XXX")=(9p-4q)(5p+7q)`

Replacing `p` and `q` with `x^2` and `y^2` respectively
and
Noting that the first of these factors is the difference of squares
`color(white)("XXX")=(3x+2y)(3x+2y)(5x^2+7y^2)`