Answered

What is the factored form of the expression?

s4 – 16

A(s - 2)2(s + 2)2
B(s - 2)(s + 2)
C(s - i)(s + i)(s - 2)(s + 2)
D(s^2 + 4)(s + 2)(s - 2)

Verified Answer :

Panoyin

s⁴ - 16
s⁴ + 4s² - 4s² - 16
s²(s²) + s²(4) - 4(s²) - 4(4)
s²(s² + 4) - 4(s² + 4)
(s² - 4)(s² + 4)
(s² + 2s - 2s - 4)(s² + 4)
(s(s) + s(2) - 2(s) - 2(2))(s² + 4)
(s(s + 2) - 2(s + 2))(s² + 4)
(s - 2)(s + 2)(s² + 4)

The answer is D.

Answer:

\((s^{2}+ 4)\) (s + 2) (s -2).

Step-by-step explanation:

Given  : \(s^{4} - 16\).

To find : What is the factored form of the expression.

Solution : We have given that  \(s^{4} - 16\).

By \(a^{2} - b^{2} = (a-b) (a+b)\).

\(s^{4} - 16\)

\((s^{2})^{2} - 4^{2}\) = \((s^{2} -4) (s^{2}+ 4)\)

We can write  \((s^{2} -4)\) as \(s^{2} - 2^{2}\)

\(s^{2} - 2^{2}\) = (s + 2) (s -2).

Then ,

\((s^{2})^{2} - 4^{2}\)  = \((s^{2}+ 4)\)  (s + 2) (s -2).

Therefore,  \((s^{2}+ 4)\)  (s + 2) (s -2).

Related Questions