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?

(3 – 6y²)(y² + 2) = - 6y⁴ - 9y² + 6

Step-by-step explanation:

Given the expression

3-6y² and y²+2

We have to find the product of 3-6y² and y²+2

Clara's Solution:

(3 – 6y²)(y² + 2) = 3(y²) + (–6y²)(2)

                          = 3y² – 12y²

                          = -9y²

NO!

The student's work is INCORRECT!

Clara did not imply the correct distribution of multiplying the terms in the first step.

Here is the correct solution:

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

                          = 3y² – 12y² + 6 - 6y⁴

                           = - 6y⁴ - 9y² + 6

Therefore,

(3 – 6y²)(y² + 2) = - 6y⁴ - 9y² + 6

step-by-step explanation: