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

Option C. is the correct option.

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.

Hope it helps:)