Answer:
B. (b+3c)+(b+3c)
C. 2(b)+2(3c)
Step-by-step explanation:
we have
[tex]2(b+3c)[/tex]
Distribute the number 2
[tex]2(b+3c)=2b+2(3c)=2b+6c[/tex]
Verify each case
case A) 3(b+2c)
distribute the number 3
[tex]3(b+2c)=3b+3(2c)=3b+6c[/tex]
[tex]3b+6c \neq 2b+6c[/tex]
therefore
Choice A is not equivalent to the given expression
case B) (b+3c)+(b+3c)
Combine like terms
[tex]b+3c)+(b+3c)=(b+b)=(3c+3c)=2b+6c[/tex]
[tex]2b+6c= 2b+6c[/tex]
therefore
Choice B is equivalent to the given expression
case C) 2(b)+2(3c)
Multiply both terns by 2
[tex]2(b)+2(3c)=2b+6c[/tex]
[tex]2b+6c= 2b+6c[/tex]
therefore
Choice C is equivalent to the given expression
