To solve the expression \((2a + 5b)3\), I'll walk through each step in draft form.

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### Draft 1: Understand the Expression
The expression given is:
\[
(2a + 5b)3
\]
which implies multiplying \(2a + 5b\) by \(3\).

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### Draft 2: Apply the Distributive Property
To simplify, apply the distributive property:
\[
3 \cdot (2a + 5b) = (3 \cdot 2a) + (3 \cdot 5b)
\]

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### Draft 3: Perform Multiplications
Now, calculate each multiplication:
1. \(3 \cdot 2a = 6a\)
2. \(3 \cdot 5b = 15b\)

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### Draft 4: Combine the Results
Combine the results to get the simplified expression:
\[
6a + 15b
\]

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### Final Answer
The simplified form of \((2a + 5b)3\) is:
\[
6a + 15b
\]

Would you like a deeper explanation or have any questions?

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1. How does the distributive property work in algebra?
2. Why does multiplying distribute over addition in this way?
3. What if the expression was \((2a + 5b)3c\)?
4. How would this change if we were adding terms instead of multiplying?
5. Can the distributive property apply to expressions with subtraction?

**Tip:** When simplifying, remember to apply operations carefully in order of operations (PEMDAS).

Explore a step-by-step solution to simplify the algebraic expression (2a + 5b)3. Learn how to apply the distributive property to expand and simplify expressions in algebra, suitable for students in Grades 6-8.

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