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

Oct 24, 2015

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

$- 7 {x}^{4} + 567 {x}^{2} = - 7 {x}^{2} \left(x - 9\right) \left(x + 9\right)$

#### Explanation:

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

$- 7 {x}^{4} + 567 {x}^{2} = - 7 {x}^{2} \left({x}^{2} - 81\right) = - 7 {x}^{2} \left({x}^{2} - {9}^{2}\right) = - 7 {x}^{2} \left(x - 9\right) \left(x + 9\right)$

...using the difference of squares identity

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