Question

What is the factored form of the expression?

s^4 – 16
A. (s - 2)^2(s + 2)^2

B. (s - 2)(s + 2)

C. (s - i)(s + i)(s - 2)(s + 2)
D. (s - 2i)(s + 2i)(s - 2)(s + 2)

Answer 1

i think it is not (A)

Answer 2

Think of \(s^4 - 16\) as \((s^2)^2 - (2^2)^2\). Now use difference of squares formula.

Answer 3

how do i do that

Answer 4

i think A

Answer 5

Y

Answer 6

\[ a^2 - b^2 = (a + b)(a - b) \implies (s^2)^2 - (2^2)^2 =(s^2 + 2^2)(s^2 - 2^2)\]No, @moha_10

Answer 7

coz s is power to 4 so the corect answer is A as i think

Answer 8

am i right ?@ParthKohli

Answer 9

No @moha_10
We have \((s^2 + 2^2)(s^2 - 2^2)\) so far.
Now we can factor \(s^2 - 2^2\) easily.

Answer 10

\[a^2 -b^2 = (a + b)(a - b) \implies s^2 - 2^2 =\cdots \]

Answer 11

you lost me with that

Answer 12

okay parth by logic i can say A

Answer 13

@moha_10
Follow @ParthKohli 's logic:
a2−b2=(a+b)(a−b)⟹(s2)2−(22)2=(s2+22)(s2−22)
(s^2-2^2) <=> (s+2)(s-2)
But by the same token (s^2+2^2) can also be factorized into:
(s^2+2^2) <=> (s+2i)(s-2i)
where i^2=-1.

Answer 14

\[s^4-16=\left(s^2+4\right)\left(s^2-4\right)=\left(s^2+4\right)(s-2) (s+2) \]