How do you factor $- 7 x^{4} + 567 x^{2}$ $-7x^4 + 567x^2$ ?

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How do you factor $- 7 x^{4} + 567 x^{2}$ $-7x^4 + 567x^2$ ?

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Answer 1 · 2015-10-24T21:47:22

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

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

Explanation:

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

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

...using the difference of squares identity

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

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How do you factor $- 7 x^{4} + 567 x^{2}$ $-7x^4 + 567x^2$ ?

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How do you factor $- 7 x^{4} + 567 x^{2}$ $-7x^4 + 567x^2$ ?