Question

Factor completely, then place the answer in the proper location on the grid. 9x 4 -225y^8

Answer 1

see explanation

Explanation:

Given

9
`x^(4)` - 225
`y^(8)` ← factor out 9 from each term

= 9(
`x^(4)` - 25
`y^(8)` ) ← difference of squares

Difference of squares factors in general as

a² - b² = (a - b)(a + b)

`x^(4)` = (x² )² ⇒ a = x²

25
`y^(8)` = (5
`y^(4)` )² ⇒ b = 5
`y^(4)`

Hence

`x^(4)` - 25
`y^(8)`

= (
`x^(4)` -5
`y^(4)` )(
`x^(4)` + 5
`y^(4)` )

Thus

9
`x^(4)` - 225
`y^(8)`

= 9 (
`x^(4)` - 5
`y^(4)` )(
`x^(4)` + 5
`y^(4)` )

Answer 2

`9(x^2+5y^4)(x^2-5y^4)`

Explanation:

`9x^4 -225y^8`

Greatest common factor is 9

`9x^4 -225y^8`

`9(x^4 -25y^8)`

Now we write the temrs in sqaure form

`9((x^2)^2-(5y^4)^2)`

Now apply a^2-b^2 formula

`a^2-b^2=(a+b)(a-b)`

`9((x^2)^2-(5y^4)^2)`

`9(x^2+5y^4)(x^2-5y^4)`

Its completely factored