Answer:
The expressions that completely factored are:
[tex]32y^{10}-24[/tex] = 8([tex]y^{10}-3[/tex]) ⇒ 2nd
[tex]16y^{5}+12y^{3}=4y^{3}(4y^{2}+3)[/tex] ⇒ 4th
Step-by-step explanation:
Complete factorization means the terms in the bracket has no common factor
∵ The expression is 18y³ - 6y
- Find the greatest common factor of the numbers and the variable
∵ The greatest common factor of 18 and 6 is 6
∵ The greatest common factor of y³ and y is y
∴ The greatest common factor is 6y
- Divide each term by 6y to find the terms in the bracket
∴ 18y³ - 6y = 6y(3y² - 1) ⇒ not the same with the answer
∵ The expression is [tex]32y^{10}-24[/tex]
∵ The greatest common factor of 32 and 24 is 8
∴ The greatest common factor is 8
- Divide each term by 8 to find the terms in the bracket
∴ [tex]32y^{10}-24[/tex] = 8( [tex]y^{10}-3[/tex]) ⇒ the same with the answer
∴ The expression [tex]32y^{10}-24[/tex] = 8([tex]y^{10}-3[/tex]) is completely factored
∵ The expression is [tex]20y^{7}+10y^{2}[/tex]
∵ The greatest common factor of 20 and 10 is 10
∵ The greatest common factor of [tex]y^{7}[/tex] and y² is y²
∴ The greatest common factor is 10y²
- Divide each term by 10y² to find the terms in the bracket
∴ [tex]20y^{7}+10y^{2}=10y^{2}(2y^{5}+1)[/tex] ⇒ not the same with the answer
∵ The expression is [tex]16y^{5}+12y^{3}[/tex]
∵ The greatest common factor of 16 and 12 is 4
∵ The greatest common factor of [tex]y^{5}[/tex] and y³ is y³
∴ The greatest common factor is 4y³
- Divide each term by 4y³ to find the terms in the bracket
∴ [tex]16y^{5}+12y^{3}=4y^{3}(4y^{2}+3)[/tex] ⇒ the same with the answer
∴ The expression [tex]16y^{5}+12y^{3}=4y^{3}(4y^{2}+3)[/tex] is completely factored
The expressions that completely factored are:
[tex]32y^{10}-24[/tex] = 8([tex]y^{10}-3[/tex])
[tex]16y^{5}+12y^{3}=4y^{3}(4y^{2}+3)[/tex]
