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

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Answer 1 · 2015-12-28T16:37:40

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

$-50x^2+x^4+49 = (x-7)(x+7)(x-1)(x+1)$

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

$= (x^2)^2-50(x^2)+49$

$= (x^2)^2-(49+1)(x^2)+(49xx1)$

$= (x^2-49)(x^2-1)$

$= (x^2-7^2)(x^2-1^2)$

$= (x-7)(x+7)(x-1)(x+1)$

using the difference of squares identity:

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

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