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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. 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.

Respuesta :

1. The term [tex]-2(x-2)^2[/tex] is simplified by first squaring the expression (x – 2).

TRUE

2. The simplified product is a binomial. TRUE

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

TRUE

4. The parentheses are eliminated through multiplication.  TRUE

5. The final simplified product is  [tex]-28x^2 + 8x - 8[/tex] FALSE

Step-by-step explanation:

Here, the given expression is :

[tex]F(x) = 3x(x- 12x) + 3x^2-2(x-2)^2[/tex]

Now, let us first solve the given expression step wise:

[tex]F(x) = 3x(x-12x) +3x^2 -2(x-2)^2\\= 3x(-11x) +3x^2 -2(x^2 +4 -4x)\\= -33x^2 + 3x^2 -2x^2 -8+8x\\= -32x^2 +8x - 8\\\implies F(x) = -32x^2 +8x - 8[/tex]

Now, here the given statements are:

1. The term [tex]-2(x-2)^2[/tex] is simplified by first squaring the expression (x – 2).

TRUE

2. The simplified product is a binomial. TRUE

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

TRUE

4. The parentheses are eliminated through multiplication.  TRUE

5. The final simplified product is  [tex]-28x^2 + 8x - 8[/tex] FALSE

As the simplified expression is: [tex](-32x^2 +8x -8)[/tex]

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