Question

How do you factor `4x^4 - 64`?

Answer 1

`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)`