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:

Simplify the expression

$$
LATEXBLOCK0
$$

Evaluate the statements

• "The term \(-2(x-2)^2\) is simplified by first squaring the expression \(x-2\)": True (order of operations requires evaluating exponents before multiplying by \(-2\)).
• "The simplified product is a binomial": False (the result \(-32x^2 + 8x - 8\) is a trinomial).
• "After multiplying, the like terms are combined by adding and subtracting": True (combining \(-33x^2 + 3x^2 - 2x^2\)).
• "The parentheses are eliminated through multiplication": True (distributing \(3x\) and \(-2\) eliminates parentheses).
• "The final simplified product is \(-28x^2 + 8x - 8\)": False (the correct simplified product is \(-32x^2 + 8x - 8\)).

Select the three true options

The three true statements are:

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

Answer:

• The term \(-2(x - 2)^2\) is simplified by first squaring the expression \(x - 2\) (Correct answer)
• The simplified product is a binomial
• After multiplying, the like terms are combined by adding and subtracting (Correct answer)
• The parentheses are eliminated through multiplication (Correct answer)
• The final simplified product is \(-28x^2 + 8x - 8\)