Let's simplify the expression step by step:
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First, distribute the 2 in the first term: \[ 2(10b + 4) = 20b + 8 \]
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Next, we can rewrite the second term, remembering to distribute the negative sign: \[ -(b - 2) = -b + 2 \]
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Now, we can combine both results: \[ 20b + 8 - b + 2 \]
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Combine like terms:
- Combine the \(b\) terms: \(20b - b = 19b\)
- Combine the constant terms: \(8 + 2 = 10\)
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Therefore, the simplified expression is: \[ 19b + 10 \]
So, \(2(10b + 4) - (b - 2) = 19b + 10\).