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).