Question

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

Answer 1

- 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.

Answer 2

The correct answer is,

x⁴ - 16 = (x² + 4)(x + 2)(x - 2)

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)