Answer:
[tex]-1(12w-6)[/tex]
Step-by-step explanation:
we have
[tex](12w+6)[/tex]
Verify each expression
case 1) [tex]-1(12w-6)[/tex]
Apply distributive property
Remember that
[tex](-1)(-1)=1[/tex]
[tex](-1)(1)=-1[/tex]
[tex]-1(12w)-1(-6)[/tex]
[tex]-12w+6[/tex]
compare with the given expression
[tex]-12w+6 \neq (12w+6)[/tex] ----> are not equivalent
case 2) [tex]2(3+6w)[/tex]
Apply distributive property
[tex]2(3)+2(6w)[/tex]
[tex]6+12w[/tex]
compare with the given expression
[tex]6+12w=(12w+6)[/tex] ---> are equivalent
case 3) [tex]6(1+2w)[/tex]
Apply distributive property
[tex]6(1)+6(2w)[/tex]
[tex]6+12w[/tex]
compare with the given expression
[tex]6+12w=(12w+6)[/tex] ---> are equivalent
case 4) [tex]-1(-12w-6)[/tex]
Apply distributive property
Remember that
[tex](-1)(-1)=1[/tex]
[tex](-1)(1)=-1[/tex]
[tex]-1(-12w)-(1)(-6)[/tex]
[tex]12w+6[/tex]
compare with the given expression
[tex]12w+6=(12w+6)[/tex] ---> are equivalent
