Question

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

Answer 1

Answer:

see explanation

Step-by-step 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

Answer:

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

Step-by-step 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