Question

type the correct answer in each box.

consider the expressions shown below.

a	b	c

complete each of the following statements with the letter that represents the expression.

\\((3x^2 - 6x + 11) - (10x^2 - 4x + 6)\\) is equivalent to expression .
\\((-3x^2 - 5x - 3) - (-10x^2 - 7x + 2)\\) is equivalent to expression .
\\((12x^2 + 6x - 5) - (5x^2 + 8x - 12)\\) is equivalent to expression .

Explanation:

⚡ Using what you learned: adding and subtracting polynomials

Step 1: Simplify the first expression

$$ (3x^2 - 6x + 11) - (10x^2 - 4x + 6) $$

$$ = 3x^2 - 6x + 11 - 10x^2 + 4x - 6 $$

$$ = (3x^2 - 10x^2) + (-6x + 4x) + (11 - 6) $$

$$ = -7x^2 - 2x + 5 $$

This matches expression A.

Step 2: Simplify the second expression

$$ (-3x^2 - 5x - 3) - (-10x^2 - 7x + 2) $$

$$ = -3x^2 - 5x - 3 + 10x^2 + 7x - 2 $$

$$ = (-3x^2 + 10x^2) + (-5x + 7x) + (-3 - 2) $$

$$ = 7x^2 + 2x - 5 $$

This matches expression C.

Step 3: Simplify the third expression

$$ (12x^2 + 6x - 5) - (5x^2 + 8x - 12) $$

$$ = 12x^2 + 6x - 5 - 5x^2 - 8x + 12 $$

$$ = (12x^2 - 5x^2) + (6x - 8x) + (-5 + 12) $$

$$ = 7x^2 - 2x + 7 $$

This matches expression B.

Answer:

• First statement: A
• Second statement: C
• Third statement: B