Simplify the expression 3x(x – 12x) + 3x2 – 2(x – 2)2. which statements are true about the process and simplified product? check all that apply.
1. the term –2(x – 2)2 is simplified by first squaring the expression x – 2.
2. the simplified product is a binomial.
3. after multiplying, the like terms are combined by adding and subtracting.
4. the parentheses are eliminated through multiplication.
5. the final simplified product is –28x2 +8x – 8.

1,3,4

Step-by-step explanation:

Given expression

3x(x-12x)+3x^2-2(x-2)^2

To solve the expression the whole square if x-2 will be evaluated first:

=3x(x-12x)+3x^2-2(x^2-4x+4)

Then, solving the brackets:

=3x(-11x)+3x^2-2x^2+8x-8

= -33x^2+3x^2-  2x^2+8x-8

= -32x^2+8x-8

Now lets look at the options one by one:

1. The term –2(x – 2)2 is simplified by first squaring the expression x – 2.

Statement 1 is true as the square will be solved first.

2. The simplified product is a binomial.

Statement 2 is false as the resulting expression is trinomial.

3. After multiplying, the like terms are combined by adding and subtracting.

Statement 3 is correct as the like terms with same variables are added.

4. The parentheses are eliminated through multiplication.

Statement 4 is correct. The brackets are solved by multiplying the integers into the brackets.

5. The final simplified product is –28x2 +8x – 8.

Statement 5 is false as the result is = -32x^2+8x-8  ..

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