Question

How do you factor `-7x^4 + 567x^2`?

Answer 1

Separate out the common factor `-7x^2` then use the difference of squares identity to find:

`-7x^4+567x^2 = -7x^2(x-9)(x+9)`

Explanation:

Both `-7x^4` and `567x^2` are divisible by `-7x^2`, so separate it out as a factor to find:

`-7x^4+567x^2 = -7x^2(x^2-81) = -7x^2(x^2-9^2) = -7x^2(x-9)(x+9)`

...using the difference of squares identity

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