Question

Please Help me! 15 Points!

Which expressions are equivalent to 2(b + 3c) ?
A: 3(b+2c)
B: (b + 3c) + (b + 3c)
C: 2(b) + 2(3c)

Answer 1

B. (b+3c)+(b+3c)

C. 2(b)+2(3c)

Step by Step instructions:

we have

2 (b+3c)

Distribute the number 2

2(b+3c) = 26 + 2(3c) = 26 + 6c

Verify each case

Case A) 3(b+2c)

distribute the number 3

3(b + 2c) = 36 + 3(2c) = 36 + 6c

3b + 6c is NOT equal to 2b + 6c

therefore

Choice A is not equivalent to the given expression

Case B) (b+3c)+(b+3c)

Combine like terms

b + 3c) + (b + 3c) = (b + b) = 3c + 3c = 26 + 6c

2b + 6c = 26 + 6c

therefore

Choice B is equivalent to the given expression

Case C) 2(b)+2(3c)

Multiply both terms by 2

2(b) + 2(3c) = 2b + 6c

2b + 6c = 26 + 6c

therefore

Choice C is equivalent to the given expression

Answer 2

B. (b+3c)+(b+3c)

C. 2(b)+2(3c)

Step by Step instruction :)))

we have

2 (b+3c)

Distribute the number 2

2(b+3c) = 26 + 2(3c) = 26 + 6c

Verify each case

Case A) 3(b+2c)

distribute the number 3

3(b + 2c) = 36 + 3(2c) = 36 + 6c

3b + 6c is NOT equal to 2b + 6c

therefore

Choice A is not equivalent to the given expression

Case B) (b+3c)+(b+3c)

Combine like terms

b + 3c) + (b + 3c) = (b + b) = 3c + 3c = 26 + 6c

2b + 6c = 26 + 6c

therefore

Choice B is equivalent to the given expression

Case C) 2(b)+2(3c)

Multiply both terms by 2

2(b) + 2(3c) = 2b + 6c

2b + 6c = 26 + 6c

therefore

Choice C is equivalent to the given expression

♡Hope it helps♡