Question

which polynomial represents the sum below?
$(16x^2 - 16) + (-12x^2 - 12x + 12)$

a. $28x^2 - 28x - 12$
b. $16x^2 - 28x - 16$
c. $4x^2 - 12x + 28$
d. $4x^2 - 12x - 4$

Explanation:

Step1: Remove parentheses

Remove the parentheses from the expression \((16x^2 - 16)+(-12x^2 - 12x + 12)\), we get \(16x^2 - 16 - 12x^2 - 12x + 12\).

Step2: Combine like terms

• For the \(x^2\) terms: \(16x^2- 12x^2=(16 - 12)x^2 = 4x^2\)
• For the \(x\) terms: There is only \(-12x\)
• For the constant terms: \(-16 + 12=-4\)

Combining these results, we have \(4x^2-12x - 4\)

Answer:

D. \(4x^2 - 12x - 4\)