Let's simplify the polynomial expression \( b(6.5a - 35b) - 1.7a(2b) \).
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Distribute \( b \) in the first term: \[ b(6.5a - 35b) = b \cdot 6.5a - b \cdot 35b = 6.5ab - 35b^2 \]
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Distribute \( -1.7a \) in the second term: \[ -1.7a(2b) = -3.4ab \]
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Now, combine the two results: \[ 6.5ab - 35b^2 - 3.4ab \]
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Combine like terms (the terms with \( ab \)): \[ (6.5ab - 3.4ab) - 35b^2 = 3.1ab - 35b^2 \]
So, the simplified form of the expression is: \[ \boxed{3.1ab - 35b^2} \]