Question

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.

Answer 1

Given: The algebraic expression 3x(x – 12x) + 3x² – 2(x – 2)²    --------(i)

To prove: The final simplified product = –28x² +8x – 8.

Solution:

Step No. 1

First, we shall expand the term (x – 2)² by using Identity (a-b)²= a² + b² - 2ab

So, (x – 2)² = x² + 4 - 4x

From given expression (i)

3x(x – 12x) + 3x² – 2(x² + 4 - 4x)  --------(ii)

Step No. 2

Now, we shall multiply by the terms within the parentheses in (ii)

(3x² – 36x²) + 3x² – (2x² + 8 - 8x)  --------(iii)

Step No. 3

Now, we shall simplify the terms within the  parentheses in (iii)

(– 33x²) + 3x² – (2x² + 8 - 8x)  --------(iv)

Step No. 4

Now, we shall open the  parentheses to eliminate parentheses in (iv)

– 33x² + 3x² – 2x² - 8 + 8x   --------(v)

Step No. 5

Now, we shall add and subtract the like terms in (v)

– 28x² + 8x -8  --------(vi)

Hence, the simplified expression will be – 28x² + 8x -8

Answer 2

Answer:

Option 1,3 and 4

Step-by-step explanation:

Given: The algebraic expression  $3x(x-12x) + 3x^2-2(x-2)^2$

To find :  Which statements are true about the process and simplified product?

Solution :

First we solve the algebraic expression,

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

Solve the square term,

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

Open the parentheses by multiplication,

$=3x^2-36x^2+3x^2-2x^2-8+8x$

Add or subtract the like terms,

$=-32x^2+8x-8$

So, looking at the steps

Correct statements are:

• The term  $- 2(x - 2)^2$ is simplified by first squaring the expression x-2.

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

• The parenthesis are eliminated through multiplication.

Therefore, Option 1,3 and 4 are correct.