Question

Factor the polynomial expression 16y^4-256x^12

Answer 1

see explanation

Explanation:

Given

16
`y^(4)` - 256
`x^(12)` ← factor out 16 from each term

= 16(
`y^(4)` - 16
`x^(12)` ) ← difference of squares which factors in general as

a² - b² = (a - b)(a + b), thus

`y^(4)` - 16
`x^(12)`

= (y² )² - (4
`x^(6)` )²

= (y² - 4
`x^(6)` )(y² + 4
`x^(6)` )

Now y² - 4
`x^(6)` ← is also a difference of squares

= y² - (2x³)²

= (y - 2x³)(y + 2x³)

Thus

16
`y^(4)` - 256
`x^(12)`

= 16(y - 2x³)(y + 2x³)(y² + 4
`x^(6)` )

Answer 2

Explanation:

4y^2+16x^6, 2y, 4x^3, 2y, 4x^3