Question

What is the completely factored form of the expression 16x^4 -y^4 Describe the method(s) of factoring you used.

Answer 1

`(2x -y)(2x+y)(4x^2+y^2)` via difference of squares

Explanation:

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

• Rewrite
`16x^(4) - y^(4)` as
`(4x^(2) )^(2) - (y^2 )^2`.

The difference of squares can be factored using the rule:
`a^2 - b^2=(a - b)(a+b).`

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

• Consider
`4x^2 - y^2`. Rewrite
`4x^2 - y^2` as
`(2x)^2 - y^2`.

The difference of squares can be factored using the rule:
`a^2 - b^2=(a - b)(a+b).`

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

• Rewrite the complete factored expression.

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

Answer 2

Explanation:

`16x^4 - y^4`

`(4y^2)^2 - (y^2)^2\\`

`= ((2y)^2)^2 - ((y)^2)^2`