To simplify the expression \( 4(2y - 6) + 3(5y + 10) \), we will distribute the constants 4 and 3 to the expressions inside the parentheses.
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Distribute the 4 in the first term: \[ 4(2y) - 4(6) = 8y - 24 \]
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Distribute the 3 in the second term: \[ 3(5y) + 3(10) = 15y + 30 \]
Now, we can combine both results: \[ 8y - 24 + 15y + 30 \]
Next, combine like terms:
- Combine the \(y\) terms: \(8y + 15y = 23y\)
- Combine the constant terms: \(-24 + 30 = 6\)
Putting it all together: \[ 23y + 6 \]
Thus, the simplified expression is: \[ \boxed{23y + 6} \]