Which of the following expressions are equivalent to 2(4f + 2g) ? Select ALL that apply.

Rationale

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

To determine the expressions equivalent to 2(4f + 2g), we can simplify the original expression. Distributing 2 results in 8f + 4g. Both A and F match this simplified form, confirming their equivalence.

A (4 * (2f + g)) CORRECT

When we distribute 4 in this expression, we get 8f + 4g. This matches our simplified expression from 2(4f + 2g), confirming that this choice is indeed equivalent.

B (4(2f + 2g)) YOUR ANSWER

Distributing 4 yields 8f + 8g. This result differs from 8f + 4g, indicating that this expression is not equivalent to 2(4f + 2g).

C (2f(4 + 2g)) YOUR ANSWER

Distributing 2f leads to 8f + 4fg. The presence of the term 4fg introduces a variable factor that does not appear in the original expression, proving this choice is not equivalent.

D (16f + 4g) YOUR ANSWER

This expression does not match the simplified form, as it suggests a total of 16f, which is twice the coefficient of f in the original equation. Hence, this choice is not equivalent.

E (8f + 2g) YOUR ANSWER

Here, 8f + 2g does not match our simplified expression, as the coefficient of g is only 2 instead of 4. Therefore, this is also not equivalent.

F (8f + 4g) CORRECT

This expression exactly matches the result from simplifying 2(4f + 2g), confirming its equivalence.

Conclusion

The expressions equivalent to 2(4f + 2g) are those that simplify to 8f + 4g. Choices A and F both meet this criterion, while the others fail to match due to discrepancies in coefficients or additional variable terms. Understanding these simplifications is essential for recognizing equivalent expressions in algebra.

Which of the following expressions are equivalent to 2(4f + 2g) ? Select ALL that apply.

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

Related Questions

Related Quizzes

How familiar were you with this question?

Report an Issue

Rate this Practice Test