Question

Which expression is equivalent to this polynomial?

16x2 + 4
A.
(4x + 2i)(4x − 2i)
B.
(4x + 2)(4x − 2)
C.
(4x + 2)2
D.
(4x − 2i)2

Answer 1

Explanation:

the answer is A

Answer 2

A.

Explanation:

C and D do not create any x² terms when doing the multiplications. so, they are out.

B stands for (a+b)×(a-b) = a² - b².

so, that would give us a "-4" at the end and is not fitting to the "+4" term at the end of the original expression.

that leaves us with A.

let's verify :

(4x+2i)(4x-2i)

it follows the same rule as B :

(a+b)(a-b) = a² - b²

a = 4x

b = 2i

you remember, i = sqrt(-1).

so, we get

(4x)² - (2i)² = 16x² - 4×(sqrt(-1))² = 16x² - 4×(-1) = 16x²+4

bingo !