# How do you factor -50x^2 + x^4 + 49?

Dec 28, 2015

Factor as a quadratic in ${x}^{2}$, then use the difference of squares identity twice to find:

$- 50 {x}^{2} + {x}^{4} + 49 = \left(x - 7\right) \left(x + 7\right) \left(x - 1\right) \left(x + 1\right)$

#### Explanation:

$- 50 {x}^{2} + {x}^{4} + 49$

$= {\left({x}^{2}\right)}^{2} - 50 \left({x}^{2}\right) + 49$

$= {\left({x}^{2}\right)}^{2} - \left(49 + 1\right) \left({x}^{2}\right) + \left(49 \times 1\right)$

$= \left({x}^{2} - 49\right) \left({x}^{2} - 1\right)$

$= \left({x}^{2} - {7}^{2}\right) \left({x}^{2} - {1}^{2}\right)$

$= \left(x - 7\right) \left(x + 7\right) \left(x - 1\right) \left(x + 1\right)$

using the difference of squares identity:

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