(a)(f + g)(3) = ? (Simplify your answer.)
Understand the Problem
The question is asking for the simplification of the expression (a)(f + g)(3). This involves applying the distributive property to combine the terms in a simplified form.
Answer
The simplified expression is $3af + 3ag$.
Answer for screen readers
The simplified expression is $3af + 3ag$.
Steps to Solve
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Identify the expression to simplify We have the expression $(a)(f + g)(3)$. To simplify, we'll use the distributive property.
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Apply the distributive property Distribute the term (3) to the expression ((f + g)): $$ (f + g)(3) = 3f + 3g $$
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Combine with remaining terms Now include the (a) term by distributing it: $$ a(3f + 3g) = 3af + 3ag $$
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Write the final simplified expression Thus, the fully simplified form of the original expression is: $$ 3af + 3ag $$
The simplified expression is $3af + 3ag$.
More Information
This result shows how to combine and simplify expressions using the distributive property. It's a fundamental concept in algebra that allows us to manage expressions with multiple terms effectively.
Tips
- Forgetting to distribute every term in the expression can lead to incomplete answers. Ensure that each factor is accounted for during distribution.
- Misplacing parentheses or changing the order of terms during simplification can also cause errors. Always follow the order of operations carefully.
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