Answer:
[tex]-2(16xy - 10y + 7)[/tex]
Step-by-step explanation:
We analyze the options to compare which factorization gives us the result we are looking for:
we develop the expression:
[tex]2(16xy + 10y + 7)=2*16xy+2*10y+2*7\\2(16xy + 10y + 7)=32xy+20+14[/tex]
some signs are wrong, so A) is not the right choice.
we develop the expression:
[tex]-2(-16xy + 10y + 7)=-2*(-16xy)-2*10y-2*7\\-2(-16xy + 10y + 7)=32xy-20y-14[/tex]
again, some signs are wrong, so B) is not the right choice.
we develop the expression:
[tex]2(16xy - 10y - 7)=2*16xy+2*(-10y)+2(-7)\\2(16xy - 10y - 7)=32xy-20y-14[/tex]
like in the other options, some signs are wrong, so C) is not the correct answer
we develop the expression:
[tex]-2(16xy - 10y + 7)=-2*16xy-2*(-10y)-2*7\\-2(16xy - 10y + 7)=-32xy+20y-14[/tex]
this option gives us the right expression. Thus, the factorization equivalent to [tex]-32xy+20y-14[/tex] is:
[tex]-2(16xy - 10y + 7)[/tex]
