which expressions are equivalent to $2(4f + 2g)$?\nchoose 3 answers:\na $8f + 2g$\nb $2f(4 + 2g)$\nc $8f +…

which expressions are equivalent to $2(4f + 2g)$?\nchoose 3 answers:\na $8f + 2g$\nb $2f(4 + 2g)$\nc $8f + 4g$\nd $4(2f + g)$\ne $4f + 4f + 4g$

which expressions are equivalent to $2(4f + 2g)$?\nchoose 3 answers:\na $8f + 2g$\nb $2f(4 + 2g)$\nc $8f + 4g$\nd $4(2f + g)$\ne $4f + 4f + 4g$

Answer

Explanation:

Step1: Simplify the original expression

Using the distributive property (a(b + c)=ab+ac), for (2(4f + 2g)), we have (2\times4f+2\times2g = 8f + 4g).

Step2: Analyze Option A

Option A is (8f + 2g), which is not equal to (8f + 4g), so A is incorrect.

Step3: Analyze Option B

Expand (2f(4 + 2g)) using the distributive property: (2f\times4+2f\times2g=8f + 4fg), which is not equal to (8f + 4g), so B is incorrect.

Step4: Analyze Option C

Option C is (8f + 4g), which is the same as the simplified original expression, so C is correct.

Step5: Analyze Option D

Expand (4(2f+g)) using the distributive property: (4\times2f + 4\times g=8f+4g), which is equal to the simplified original expression, so D is correct.

Step6: Analyze Option E

Simplify (4f + 4f+4g): combine like terms (4f+4f = 8f), so the expression becomes (8f + 4g), which is equal to the simplified original expression, so E is correct.

Answer:

C. (8f + 4g), D. (4(2f + g)), E. (4f + 4f + 4g)