Question 26

A) 4 * (2f + g) and F) 8f + 4g are equivalent to 2(4f + 2g).

Both expressions A and F are equivalent to the original expression 2(4f + 2g) upon simplification.

A) 4 * (2f + g)

This expression can be simplified as follows: 4 * (2f + g) = 4*2f + 4*g = 8f + 4g. This matches the form of the original expression after expansion and is therefore equivalent.

B) 4(2f + 2g)

When simplifying this expression, we have 4*(2f + 2g) = 4*2f + 4*2g = 8f + 8g. This result does not match the original expression 2(4f + 2g) since it introduces an additional term (8g) that is not present in the original.

C) 2f(4 + 2g)

This expression can be simplified to 2f*4 + 2f*2g = 8f + 4fg. The term 4fg does not match the original expression, indicating that this option is not equivalent.

D) 16f + 4g

If we consider this expression, it does not correspond to the original expression when simplified. The original expression evaluates to 8f + 4g, making this option incorrect.

E) 8f + 2g

This expression does not match the original expression either. The original expression evaluates to 8f + 4g, indicating that the term involving g is incorrect.

F) 8f + 4g

This expression matches the result of simplifying the original expression: 2(4f + 2g) = 8f + 4g. Thus, it is indeed equivalent to the original expression.

Conclusion

The correct answers A and F are equivalent to the original expression 2(4f + 2g) upon simplification. All other options introduce discrepancies in either the coefficients or additional terms that prevent them from being equivalent to the original expression. Thus, A and F are the only valid choices.