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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