Which expression is equivalent to this polynomial?

16×2 + 4

A.

(4x + 2i)(4x − 2i)

B.

(4x + 2)(4x − 2)

C.

(4x + 2)2

D.

(4x − 2i)2

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16×2 + 4

A.

(4x + 2i)(4x − 2i)

B.

(4x + 2)(4x − 2)

C.

(4x + 2)2

D.

(4x − 2i)2

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Answer:A.

Step-by-step 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 !