Which expressions are completely factored? Select each correct answer. 32y10-24=8 (4y10-3)

16y5+12y3=4y3 (4y2+3)

20y7+10y2=5y (4y6+2y)

18y3-6y=3y (6y2-2)

The correct answers are:

32y¹⁰-24 = 8 (4y¹⁰-3); and

16y⁵+12y³ = 4y³ (4y²+3).

Explanation:

All of these are being factored by pulling out the GCF.

In the first expression, the largest number that each coefficient is divisible by is 8. Only one of these terms has a variable, so it does not come out.

Pulling 8 out (dividing by 8) leaves us with: 8 (4y¹⁰-3)

In the second expression, the GCF of the coefficients is 4. Additionally, both of them have a variable; since each has at least y³, we can factor this out as well. This makes the GCF 4y³. Pulling this out leaves us with:

4y³ (4y²+3) ²

In the third expression, a y² should have been factored out instead of just y.

In the last expression, 6y should have been factored out instead of 3y.

First option: 32y10-24=8 (4y10-3)

Second option: 16y5+12y3=4y3 (4y2+3)

1) 32y^10-24

Common factor: 8

8 (32y^10/8-24/8) = 8 (4y^10-3) Ok

2) 16y^5+12y^3

Common factor 4y^3

4y^3[ (16y^5) / (4y^3) + (12y^3) / (4y^3) ]=4y^3 (4y^2+3) Ok

3) 20y^7+10y^2

Common factor 10y^2

10y^2[ (20y^7) / (10y^2) + (10y^2) / (10y^2) ]=10y^2 (2y^5+1) No

4) 18y^3-6y

Common factor: 6y

6y[ (18y^3) / (6y) - (6y) / (6y) ]=6y (3y^2-1) No