An expression is shown below

Question

2x³y + 8xy - 4x²y - 16y

 

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

 

Part B: Rewrite the expression completely factored. 

 

(I am unsure of the difference between factoring the GFC and factoring the expression.) :-)

 

 

Answer 1

Hi Lilly,

 

2x^3y + 8xy - 4x^2y - 16y 

write it like this

2x^3y - 4x^2y + 8xy - 16y (I shuffled the terms to bring similar terms together, which will help with  factoring)

2x^2y(x - 2) + 8y(x - 2) (I factored the first two and the last two terms, respectively). This is the answer to Part A.

 

You can see that (x - 2) is a common factor. We can use that to completely factor the expression.

(x - 2)(2x^2y + 8y) This is the answer to Part B.