Question

How do you factor completely `x^4-16`?

Answer 1

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

Explanation:

Recall the factor of difference of square `a^2-b^2= (a-b)(a+b)`

We can re-write `x^4 - 16= (x^2)^2 -4^2`
`rArr (x^2 -4)(x^2+4)`
`=> (x^2 -2^2 )(x+4) =>` difference of square again
`rArr color(red)((x-2)(x+2)(x+4)`