Question

What is the completely factored form of t4 − 16?a. (t^2+4)(t^2-4)b. (t^2+4)(t+2)(t-4)c. (t^2+4)(t-2)(t-2)d. (t+2)(t+2)(t+2)(t-2)

Answer 1

`\mleft(t^2+4\mright)\mleft(t^2-4\mright)`

Step-by-step explanation:

We were given:

`t^4-16`

We will proceed to factor it as shown below:

`\begin{gathered} t^4-16 \\ Using\text{ the formula for difference of two squares}\colon a^2-b^2=\mleft(a+b\mright)\mleft(a-b\mright) \\ t^4-16\Rightarrow(t^2)^2-4^2 \\ (t^2)^2-4^2\Rightarrow(t^2+4)\mleft(t^2-4\mright) \\ (t^2+4)(t^2-4) \\ \\ \therefore(t^2+4)(t^2-4) \end{gathered}`

Hence, a. is the correct answer