To simplify the expression \((6b + 4r) - (2b + r)\), follow these steps:
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Distribute the negative sign across the second expression: \[ (6b + 4r) - (2b + r) = 6b + 4r - 2b - r \]
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Combine like terms:
- For the \(b\) terms: \(6b - 2b = 4b\)
- For the \(r\) terms: \(4r - r = 3r\)
Therefore, the simplified expression is: \[ 4b + 3r \]
So the final answer is: \[ \boxed{4b + 3r} \]