SOLUTION: 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?

Question 1119182: 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.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the distributive property says:

(a - b) * (c + d) equals a * (c + d) - b * (c + d) which is equal to:

a * c + a * d - b * c - b * d.

your expression is 3 � 6y^2 and y^2 + 2.

this would be written as (3 - 6y^2) * (y^2 + 2)

by the distributive property, this would be equal to:

3 * (y^2 + 2) - 6y^2 * (y^2 + 2), which would be equal to:

3 * y^2 + 3 * 2 - 6y^2 * y^2 - 6y^2 * 2, which would be equal to:

3y^2 + 6 - 6y^4 - 12y^2, which would then be equal to:

-9y^2 + 6 - 6y^4 after combining like terms, which would then be equal to:

-6y^4 - 9y^2 + 6 after re-arranging the terms in descending order of degree.

-6y^2 * 2 = -12y^2 so she did that correctly.

3y^2 - 12y^2 = -9y^2 so she did that correctly.

she did not, however, use the distributive property correctly.

that's your answer.

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