How do you factor 81-16x^481−16x4?

1 Answer
sente
Nov 12, 2015

Apply the difference of squares formula twice to find
81-16x^4 = (9 + 4x^2)(3+2x)(3-2x)81−16x4=(9+4x2)(3+2x)(3−2x)

Explanation:

The difference of squares formula states
x^2 - y^2 = (x+y)(x-y)x2−y2=(x+y)(x−y)

81 = 9^281=92 and 16x^4 = (4x^2)^216x4=(4x2)2

So, applying the formula,
81 - 16x^4 = 9^2 - (4x^2)^2 = (9 + 4x^2)(9 - 4x^2)81−16x4=92−(4x2)2=(9+4x2)(9−4x2)

But we are not quite done.

9 = 3^29=32 and 4x^2 = (2x)^24x2=(2x)2

So applying the formula to 9-4x^29−4x2, we get the final result of

81 - 16x^4 = (9 + 4x^2)(9 - 4x^2) = (9 + 4x^2)(3+2x)(3-2x)81−16x4=(9+4x2)(9−4x2)=(9+4x2)(3+2x)(3−2x)

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