Question

Clara found the product of 3 – 6y2 and y2 + 2. Her work is shown below. (3 – 6y2)(y2 + 2) = 3(y2) + (–6y2)(2)    = 3y2 – 12y2    = –9y2 Is the student’s work correct? No, she did not multiply –6y2 by 2 correctly.  No, she did not add 3y2 and –12y2  correctly. No, she did not use the distributive property correctly. Yes, she multiplied the binomials correctly.

Answer 1

Answer:

Option C. is the correct option.

Step-by-step explanation:

Clara found the product of (3 - 6y²) and (y² + 2) and she did it as below

(3 - 6y²)(y² + 2) = 3(y²) + (-6y²)×2 = 3y² - 12y² = -9y²

She did the step wrong as highlighted above. She did not use the distributive property correctly.

Now we will do it in a correct way.

(3 - 6y²)(y²+2) = 3(y² + 2) - 6y²(y² + 2)

= $3y^{2}+6-6y^{4}-12y^{2}=-6y^{4}-9y^{2}+6$

Therefore Option C. is the correct answer.

Answer 2

The product of (3 - 6y²) and (y² + 2) is  -6y⁴ - 9y² + 6

Product

Finding the product between two values is multiplying the values together .Therefore, the product between (3 - 6y²) and (y² + 2) is as follows:

• (3 - 6y²)(y² + 2)

(3 - 6y²)(y² + 2) = 3(y²) + 3(2) - 6y²(y²) - 6y²(2)

Therefore,

3(y²) + 3(2) - 6y²(y²) - 6y²(2) = 3y² + 6 - 6y⁴ - 12y²

3y² + 6 - 6y⁴ - 12y² = -6y⁴ - 9y² + 6

Therefore, the product of (3 - 6y²) and (y² + 2) is  -6y⁴ - 9y² + 6

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