Question

simplify the expression 3x(x - 12x) + 3x² - 2(x - 2)². which statements are true about the process and simplified product? select three options. the term -2(x - 2)² is simplified by first squaring the expression x - 2. the simplified product is a binomial. after multiplying, the like terms are combined by adding and subtracting. the parentheses are eliminated through multiplication. the final simplified product is -28x² + 8x - 8.

Explanation:

Step1: Expand $3x(x-12x)$

$3x(x-12x) = 3x^2 - 36x^2 = -33x^2$

Step2: Expand $-2(x-2)^2$

First, square $(x-2)$: $(x-2)^2 = x^2 -4x +4$
Multiply by -2: $-2(x^2 -4x +4) = -2x^2 +8x -8$

Step3: Combine all terms

Add $-33x^2$, $3x^2$, and $-2x^2 +8x -8$:
$-33x^2 +3x^2 -2x^2 +8x -8 = -32x^2 +8x -8$

Step4: Verify each statement

1. Check squaring $(x-2)$ first: Correct, as $(x-2)^2$ must be expanded first.
2. Check simplified product type: It is a trinomial, not binomial.
3. Check combining like terms: Like terms are combined via addition/subtraction. Correct.
4. Check parentheses elimination: Parentheses are removed via multiplication. Correct.
5. Check final simplified product: The correct result is $-32x^2 +8x -8$, not $-28x^2 +8x -8$.

Answer:

A. The term $-2(x - 2)^2$ is simplified by first squaring the expression $x - 2$.
B. After multiplying, the like terms are combined by adding and subtracting.
C. The parentheses are eliminated through multiplication.