Question

simplify the expression $3x(x - 12x) + 3x^2 - 2(x - 2)^2$. 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 $-28x^2 + 8x - 8$.

Explanation:

Step1: Simplify first term

$3x(x - 12x) = 3x(-11x) = -33x^2$

Step2: Expand squared term

$-2(x-2)^2 = -2(x^2 -4x +4) = -2x^2 +8x -8$

Step3: Combine all terms

$-33x^2 + 3x^2 -2x^2 +8x -8$

Step4: Combine like terms

$(-33+3-2)x^2 +8x -8 = -32x^2 +8x -8$

Step5: Verify each statement

1. For $-2(x-2)^2$, first square $x-2$: True
2. Simplified product is trinomial, not binomial: False
3. Combine like terms via addition/subtraction: True
4. Eliminate parentheses via multiplication: True
5. Final product is $-32x^2+8x-8$, not $-28x^2+8x-8$: False

Answer:

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