Question

How do you factor `16x^2-x^2y^4`?

Answer 1

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

Explanation:

First, notice that both terms have a common factor of `x^2`, so we can factor it out:

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

Focusing on just the `(16-y^4)`, notice that both of these are squared terms:

• `16=4^2`
• `y^4=(y^2)^2`

This will be useful since `(16-y^4)` is a difference of squares, which can be factored as: `a^2-b^2=(a+b)(a-b)`. Thus, we see that:

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

Note that `(4-y^2)` is also a difference of squares, since `y^2` is obviously squared and `4=2^2`. We see that:

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