To simplify the expression \((5.3a^2 - 0.4a + 9.1) - (4.2 + 3.8a^2 - 67a)\), we will first distribute the negative sign across the second set of parentheses:
\[ (5.3a^2 - 0.4a + 9.1) - 4.2 - 3.8a^2 + 67a \]
Now, we can rearrange and combine like terms. Let's group the terms by their degree:
- \(a^2\) terms: \(5.3a^2 - 3.8a^2\)
- \(a\) terms: \(-0.4a + 67a\)
- Constant terms: \(9.1 - 4.2\)
Now, let's combine each group:
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For the \(a^2\) terms: \[ 5.3a^2 - 3.8a^2 = (5.3 - 3.8)a^2 = 1.5a^2 \]
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For the \(a\) terms: \[ -0.4a + 67a = (67 - 0.4)a = 66.6a \]
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For the constant terms: \[ 9.1 - 4.2 = 4.9 \]
Combining all of these together, we get:
\[ 1.5a^2 + 66.6a + 4.9 \]
Therefore, the expression equivalent to \((5.3a^2-0.4a+9.1)-(4.2+3.8a^2-67a)\) is:
\[ \boxed{1.5a^2 + 66.6a + 4.9} \]