Questions: Simplify the expression 3 x(x-12 x)+3 x^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 -28 x^2+8 x-8.

Simplify the expression 3 x(x-12 x)+3 x^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 -28 x^2+8 x-8.
Transcript text: Simplify the expression $3 x(x-12 x)+3 x^{2}-2(x-2)^{2}$. 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 $-28 x^{2}+8 x-8$.
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Solution

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Solution Steps

Step 1: Expand the Expression

First, we expand the given expression \(3x(x - 12x) + 3x^2 - 2(x - 2)^2\).

\[ 3x(x - 12x) = 3x(-11x) = -33x^2 \]

\[ -2(x - 2)^2 = -2(x^2 - 4x + 4) = -2x^2 + 8x - 8 \]

Step 2: Combine Like Terms

Next, we combine the like terms from the expanded expression:

\[ -33x^2 + 3x^2 - 2x^2 + 8x - 8 \]

Step 3: Simplify the Expression

Now, we simplify the expression by combining the coefficients of like terms:

\[ -33x^2 + 3x^2 - 2x^2 = -32x^2 \]

So, the simplified expression is:

\[ -32x^2 + 8x - 8 \]

Final Answer

\(\boxed{-32x^2 + 8x - 8}\)

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