How do you factor 4x^4 - 64 ?

1 Answer
Jim G.
Sep 3, 2016

4(x-2)(x+2)(x^2+4)

Explanation:

The first step is to take out a color(blue)"common factor" of 4

rArr4(x^4-16)........ (A)

Now x^4-16 " is a " color(blue)"difference of squares" and in general factorises as.

color(red)(|bar(ul(color(white)(a/a)color(black)(a^2-b^2=(a-b)(a+b))color(white)(a/a)|)))........ (B)

x^4=(x^2)^2" and " 16=(4)^2rArra=x^2" and " b=4

substitute these values into (B)

rArrx^4-16=(x^2-4)(x^2+4)

Note that x^2-4 is also a color(blue)"difference of squares"

and using the method of above

rArrx^2-4=(x-2)(x+2)

substituting the values from the 2 results into (A) remembering the factor (x^2+4)

rArr4x^4-64=4(x-2)(x+2)(x^2+4)

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