How do I solve this

Question

Which expressions are completely factored?

Select each correct answer.

18y^3−6y=3y(6y^2−2)

20y^7+10y^2=5y(4y^6+2y)

32y^10−24=8(4y^10−3)

16y^5+12y3=4y^3(4y^2+3)

Answer 1

This is an exercise in figuring out the greatest common factor of the two terms on the left side of the equal sign and factoring it out.

 

18y³ - 6y has a greatest common factor of 6y. So factor 6y out of both terms to get the answer:  6y(3y² - 1).  This is not the answer you were given so this choice is not correct.

 

We'll use the same method for each of the other three choices.

 

20y⁷ + 10y² has greatest common factor 10y² so: 10y²(2y⁵ + 1) is the factored form but this is not the answer given.

 

32y¹⁰ - 24 has greatest common factor 8 so: 8(4y¹⁰ -3) is the factored form. The given answer is correct.

 

16y⁵ + 12y³ has greatest common factor 4y³ so: 4y³(4y² + 3) is the factored form. This given answer is also correct.