Question

type the correct answer in each box.
consider the expressions shown below.

a	b	c

complete the following statements with the letter that represents the expression.
$(7x^2 - 5x + 3) + (2x^2 + 3x - 1)$ is equivalent to expression \\(\square\\).
$(3x^2 - 4x - 4) + (-12x^2 + 2x + 11)$ is equivalent to expression \\(\square\\).
$(4x^2 - 3x - 9) + (5x^2 + 5x + 2)$ is equivalent to expression \\(\square\\).

Explanation:

Step1: Simplify the first expression

We have \((7x^{2}-5x + 3)+(2x^{2}+3x - 1)\). Combine like terms:
For \(x^{2}\) terms: \(7x^{2}+2x^{2}=9x^{2}\)
For \(x\) terms: \(-5x + 3x=-2x\)
For constant terms: \(3-1 = 2\)
So the simplified expression is \(9x^{2}-2x + 2\), which is expression B.

Step2: Simplify the second expression

We have \((3x^{2}-4x - 4)+(-12x^{2}+2x + 11)\). Combine like terms:
For \(x^{2}\) terms: \(3x^{2}-12x^{2}=-9x^{2}\)
For \(x\) terms: \(-4x+2x=-2x\)
For constant terms: \(-4 + 11=7\)
So the simplified expression is \(-9x^{2}-2x + 7\), which is expression A.

Step3: Simplify the third expression

We have \((4x^{2}-3x - 9)+(5x^{2}+5x + 2)\). Combine like terms:
For \(x^{2}\) terms: \(4x^{2}+5x^{2}=9x^{2}\)
For \(x\) terms: \(-3x+5x = 2x\)
For constant terms: \(-9+2=-7\)
So the simplified expression is \(9x^{2}+2x - 7\), which is expression C.

Answer:

First box: B
Second box: A
Third box: C