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

ANSWER

(t² + 4)(t + 2)(t - 2)

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:

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