Question

which expression is equivalent to (5.3a^2 - 0.4a + 9.1) - (4.2 + 3.8a^2 - 6.7a)`

Answer 1

To simplify the expression \((5.3a^2 - 0.4a + 9.1) - (4.2 + 3.8a^2 - 6.7a)\), we will first distribute the negative sign across the second set of parentheses.

Starting with the original expression:

\[
(5.3a^2 - 0.4a + 9.1) - (4.2 + 3.8a^2 - 6.7a)
\]

We can rewrite it as:

\[
5.3a^2 - 0.4a + 9.1 - 4.2 - 3.8a^2 + 6.7a
\]

Now, we'll group like terms together:

1. **For \(a^2\) terms**:

\(5.3a^2 - 3.8a^2 = (5.3 - 3.8)a^2 = 1.5a^2\)

2. **For \(a\) terms**:

\(-0.4a + 6.7a = (6.7 - 0.4)a = 6.3a\)

3. **For constant terms**:

\(9.1 - 4.2 = 4.9\)

Now, combining all of these results together, we have:

\[
1.5a^2 + 6.3a + 4.9
\]

Thus, the expression equivalent to \((5.3a^2 - 0.4a + 9.1) - (4.2 + 3.8a^2 - 6.7a)\) is:

\[
\boxed{1.5a^2 + 6.3a + 4.9}
\]