Question

What expression is equivalent to (5.3a^2-0.4a+9.1)-(4.2+3.8a^2-67a)?

Answer 1

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:

1. \(a^2\) terms: \(5.3a^2 - 3.8a^2\)
2. \(a\) terms: \(-0.4a + 67a\)
3. Constant terms: \(9.1 - 4.2\)

Now, let's combine each group:

1. For the \(a^2\) terms:
\[
5.3a^2 - 3.8a^2 = (5.3 - 3.8)a^2 = 1.5a^2
\]

2. For the \(a\) terms:
\[
-0.4a + 67a = (67 - 0.4)a = 66.6a
\]

3. 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:

\[
\boxed{1.5a^2 + 66.6a + 4.9}
\]