Which identity could be used to rewrite x^4-16

The correct answer is,

x⁴ - 16 = (x² + 4) (x + 2) (x - 2)

Step-by-step explanation:

Identity

(x² - y²) = (x + y) (x - y)

To rewrite x⁴ - 16

Using identity we can write,

x⁴ - 16 = [ (x²) ² - 4²]

= (x² + 4) (x² - 4)

= (x² + 4) (x - 2²)

= (x² + 4) (x + 2) (x - 2)

Therefore x⁴ - 16 = (x² + 4) (x + 2) (x - 2)

- Rewrite it in the form a^2-b^2, where a=x^2 and b=4.

- (x^2) ^2 - 4^2

- Use difference of squares.

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

- Rewrite {x}^{2}-4x 2 - 4 in the form {a}^{2}-{b}^{2}a 2 - b 2 , where a=xa=x and b=2b=2.

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

- Use difference of squares

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

Done.