Question

Help- ASAP please (25 points)

Write t^4 - 16 as the product of two binomials

Write t^4 - 16 as the product of three binomials.

Answer 1

(t² - 4)(t² + 4)

(t - 2)(t + 2)(t² + 4)

Explanation:

t⁴ - 16

(t²)² - 4²

(t² - 4)(t² + 4)

[t² - 2²](t² + 4)

(t - 2)(t + 2)(t² + 4)

Answer 2

(t^2 -4) (t^2 +4)

(t-2)(t+2)(t^2+4)

Explanation:

t^4 - 16

We can write this as the difference of squares

We know the dfference of squares is

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

( t^2 ^2 - 4^2) = (t^2 -4) (t^2 +4)

We can write t^2 -4 as the difference of squares

t^2 -4 = t^2 -2^2 = (t-2)(t+2)

Replacing this in

( t^2 ^2 - 4^2) = (t^2 -4) (t^2 +4) = (t-2)(t+2)(t^2+4)