Question

Which expressions are completely factored? Select each correct answer. 18y^3−6y=3y(6y^2−2) 32y^10−24=8(4y^10−3) 20y^7+10y^2=5y(4y^6+2y) 16y^5+12y^3=4y^3(4y^2+3)

Answer 1

The expressions that completely factored are:

`32y^(10)-24` = 8(
`y^(10)-3`) ⇒ 2nd

`16y^(5)+12y^(3)=4y^(3)(4y^(2)+3)` ⇒ 4th

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
`32y^(10)-24`

∵ 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

∴
`32y^(10)-24` = 8(
`y^(10)-3`) ⇒ the same with the answer

∴ The expression
`32y^(10)-24` = 8(
`y^(10)-3`) is completely factored

∵ The expression is
`20y^(7)+10y^(2)`

∵ The greatest common factor of 20 and 10 is 10

∵ The greatest common factor of
`y^(7)` and y² is y²

∴ The greatest common factor is 10y²

- Divide each term by 10y² to find the terms in the bracket

∴
`20y^(7)+10y^(2)=10y^(2)(2y^(5)+1)` ⇒ not the same with the answer

∵ The expression is
`16y^(5)+12y^(3)`

∵ The greatest common factor of 16 and 12 is 4

∵ The greatest common factor of
`y^(5)` and y³ is y³

∴ The greatest common factor is 4y³

- Divide each term by 4y³ to find the terms in the bracket

∴
`16y^(5)+12y^(3)=4y^(3)(4y^(2)+3)` ⇒ the same with the answer

∴ The expression
`16y^(5)+12y^(3)=4y^(3)(4y^(2)+3)` is completely factored

The expressions that completely factored are:

`32y^(10)-24` = 8(
`y^(10)-3`)

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