Question

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

a	b	c
-7x² - 2x + 5	7x² - 2x + 7	7x² + 2x - 5

complete each of the following statements with the letter that represents the expression.
(3x² - 6x + 11) - (10x² - 4x + 6) is equivalent to expression
(-3x² - 5x - 3) - (-10x² - 7x + 2) is equivalent to expression
(12x² + 6x - 5) - (5x² + 8x - 12) is equivalent to expression

Explanation:

Step1: Simplify the first expression

\[

$$\begin{align*} &(3x^{2}-6x + 11)-(10x^{2}-4x + 6)\\ =&3x^{2}-6x + 11-10x^{2}+4x - 6\\ =&(3x^{2}-10x^{2})+(-6x + 4x)+(11 - 6)\\ =&-7x^{2}-2x + 5 \end{align*}$$

\]
This is equivalent to expression A.

Step2: Simplify the second expression

\[

$$\begin{align*} &(-3x^{2}-5x - 3)-(-10x^{2}-7x + 2)\\ =&-3x^{2}-5x - 3 + 10x^{2}+7x - 2\\ =&(-3x^{2}+10x^{2})+(-5x + 7x)+(-3 - 2)\\ =&7x^{2}+2x - 5 \end{align*}$$

\]
This is equivalent to expression C.

Step3: Simplify the third expression

\[

$$\begin{align*} &(12x^{2}+6x - 5)-(5x^{2}+8x - 12)\\ =&12x^{2}+6x - 5-5x^{2}-8x + 12\\ =&(12x^{2}-5x^{2})+(6x - 8x)+(-5 + 12)\\ =&7x^{2}-2x + 7 \end{align*}$$

\]
This is equivalent to expression B.

Answer:

First blank: A
Second blank: C
Third blank: B