Question

What is the completely factored form of t4 − 16?Group of answer choices(t2 + 4)(t2 − 4)(t2 + 4)(t + 2)(t − 2)(t2 + 4)(t − 2)(t − 2)(t + 2)(t + 2)(t + 2)(t − 2)

Answer 1

(t² + 4)(t + 2)(t - 2)

Step-by-step explanation

To factor this expression we can use the difference of two squares:

`(t^4-16)`

To see it more clearly, let's change the variable. Let x be t², then:

`x^2=t^4`

Replacing we have:

`(x^2-16)=(x+4)(x-4)`

Replacing back x = t²:

`(t^4-16)=(t^2+4)(t^2-4)`

Now we can use the difference of two squares one more time for the second parenthesis:

`(t^2+4)(t^2-4)=(t^2+4)(t^{}+2)(t^{}-2)`