which expressions are equivalent to 2(b + 3c)? choose all answers that apply: a 3(b + 2c) b (b + 3c) + (b +…
which expressions are equivalent to 2(b + 3c)? choose all answers that apply: a 3(b + 2c) b (b + 3c) + (b + 3c) c 2(b) + 2(3c)
Answer
Explanation:
Step1: Expand the original expression
Use the distributive property (a(b + c)=ab+ac). For (2(b + 3c)), we have (2(b + 3c)=2\times b+2\times3c = 2b+6c).
Step2: Expand option A
Expand (3(b + 2c)) using the distributive property: (3(b + 2c)=3\times b+3\times2c=3b + 6c). Since (3b + 6c\neq2b+6c), option A is not equivalent.
Step3: Simplify option B
((b + 3c)+(b + 3c)=b + 3c+b + 3c=(b + b)+(3c+3c)=2b + 6c), which is equivalent to (2(b + 3c)).
Step4: Expand option C
(2(b)+2(3c)=2b+6c), which is equivalent to (2(b + 3c)).
Answer:
B. ((b + 3c)+(b + 3c)), C. (2(b)+2(3c))