Question

type the correct answer in each box. consider the expressions shown below. a: $-8x^2 - 3x + 4$, b: $8x^2 - 3x + 8$, c: $8x^2 + 3x - 4$ complete each of the following statements with the letter that represents the expression. $(3x^2 - 7x + 14) + (5x^2 + 4x - 6)$ is equivalent to expression \boxed{}. $(2x^2 - 5x - 3) + (-10x^2 + 2x + 7)$ is equivalent to expression \boxed{}. $(12x^2 - 2x - 13) + (-4x^2 + 5x + 9)$ is equivalent to expression \boxed{}.

Explanation:

Step1: Solve first expression

Combine like terms: \((3x^2 - 7x + 14) + (5x^2 + 4x - 6) = (3x^2 + 5x^2) + (-7x + 4x) + (14 - 6) = 8x^2 - 3x + 8\), which is expression B.

Step2: Solve second expression

Combine like terms: \((2x^2 - 5x - 3) + (-10x^2 + 2x + 7) = (2x^2 - 10x^2) + (-5x + 2x) + (-3 + 7) = -8x^2 - 3x + 4\), which is expression A.

Step3: Solve third expression

Combine like terms: \((12x^2 - 2x - 13) + (-4x^2 + 5x + 9) = (12x^2 - 4x^2) + (-2x + 5x) + (-13 + 9) = 8x^2 + 3x - 4\), which is expression C.

Answer:

First box: B. \(8x^2 - 3x + 8\)
Second box: A. \(-8x^2 - 3x + 4\)
Third box: C. \(8x^2 + 3x - 4\)