Question

1. (08.01, 8.02 MC) An expression is shown below: 2x3y2 + 18xy2 − 20x2y − 180y Part A: Rewrite the expression so that the GCF is factored completely. (4 points) Part B: Rewrite the expression completely factored. Show the steps of your work. (6 points) (10 points)

Answer 1

A. 2y

B. (xy − 10)(2x²y + 18y)

Explanation:

Part A: Rewrite the expression so that the GCF is factored completely.

2x³y² + 18xy² − 20x²y − 180y

Factoring y out, we have

(2x³y + 18xy − 20x² − 180)y

Factoring 2 out, we have

(x³y + 9xy − 10x² − 90)2y

So, the GCF is 2y and the expression factored is (x³y + 9xy − 10x² − 90)2y

Part B: Rewrite the expression completely factored.

2x³y² + 18xy² − 20x²y − 180y

Rearranging, we have

2x³y² − 20x²y + 18xy² − 180y

Separating them into brackets, we have

(2x³y² − 20x²y) + (18xy² − 180y)

Factorizing the expressions in bracket, we have

(xy − 10)2x²y + (xy − 10)18y

collecting like terms, we have

(xy − 10)(2x²y + 18y)