How do you factor completely: 16x^4 - 1?

1 Answer
Alan P.
Apr 25, 2018

16x^4-1=color(blue)((4x^2+1)(2x+1)(2x-1)

Explanation:

Remember
color(white)("XXX")(a^2-b^2)=(a+b)(a-b)

(16x^4-1) is of this form (with a=(4x^2) and b=1).

So
color(white)("XXX")(16x^4-1)=(4x^2+1)(4x^2-1)

...but we note that (4x^2-1) is also of this form (with a=2x and b=1)
So (4x^2-1)=(2x+1)(2x-1)

and, completely factored we have
color(white)("XXX")(16x^4-1)=(4x^2+1)(2x+1)(2x-1)

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