which expressions are equivalent to 2(4f + 2g)? choose 3 answers: a 8f + 2g b 2f(4 + 2g) c 8f + 4g d 4(2f +…
which expressions are equivalent to 2(4f + 2g)? choose 3 answers: a 8f + 2g b 2f(4 + 2g) c 8f + 4g d 4(2f + g) e 4f + 4f + 4g
Answer
Explanation:
Step1: Expand the given expression
Use the distributive property (a(b + c)=ab+ac). Here (a = 2), (b = 4f), (c = 2g). So (2(4f + 2g)=2\times4f+2\times2g=8f + 4g).
Step2: Analyze option C
Option C is (8f + 4g), which is equal to the expanded - form of the given expression.
Step3: Analyze option D
Expand (4(2f + g)) using the distributive property: (4\times2f+4\times g = 8f+4g), which is equivalent to the given expression.
Step4: Analyze option E
Simplify (4f + 4f+4g). Combine like - terms: ((4f + 4f)+4g=8f + 4g), which is equivalent to the given expression.
Answer:
C. (8f + 4g), D. (4(2f + g)), E. (4f + 4f + 4g)