Question

How do you simplify `9x^2-5x^4`?

Answer 1

`9x^2-5x^4 = x^2(3-sqrt(5)x)(3+sqrt(5)x)`

Explanation:

`9x^2-5x^2`

`color(white)("XXX")`extracting the obvious factor of `x^2`
`=x^2(9-5x^2)`

`color(white)("XXX")`remember that `(a^2-b^2) = (a-b)(a+b)`
`color(white)("XXX")`and substituting `9 = 3^2` for `a^2`
`color(white)("XXX")`and `5x^2 = (sqrt(5)x)^2` for `b^2`
`=x^2(3-sqrt(5)x)(3+sqrt(5)x)`