Question

Which factorization is equivalent to this expression? −32xy + 20y − 14 A) 2(16xy + 10y + 7) B) −2(−16xy + 10y + 7) C) 2(16xy − 10y − 7) D) −2(16xy − 10y + 7)

Answer 1

D) −2(16xy − 10y + 7)

Explanation:

Answer 2

`-2(16xy - 10y + 7)`

Explanation:

We analyze the options to compare which factorization gives us the result we are looking for:

• A)
  `2(16xy + 10y + 7)`

we develop the expression:

`2(16xy + 10y + 7)=2*16xy+2*10y+2*7\\2(16xy + 10y + 7)=32xy+20+14`

some signs are wrong, so A) is not the right choice.

• B)
  `-2(-16xy + 10y + 7)`

we develop the expression:

`-2(-16xy + 10y + 7)=-2*(-16xy)-2*10y-2*7\\-2(-16xy + 10y + 7)=32xy-20y-14`

again, some signs are wrong, so B) is not the right choice.

• C)
  `2(16xy - 10y - 7)`

we develop the expression:

`2(16xy - 10y - 7)=2*16xy+2*(-10y)+2(-7)\\2(16xy - 10y - 7)=32xy-20y-14`

like in the other options, some signs are wrong, so C) is not the correct answer

• D)
  `-2(16xy - 10y + 7)`

we develop the expression:

`-2(16xy - 10y + 7)=-2*16xy-2*(-10y)-2*7\\-2(16xy - 10y + 7)=-32xy+20y-14`

this option gives us the right expression. Thus, the factorization equivalent to
`-32xy+20y-14` is:

`-2(16xy - 10y + 7)`