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

1 answer

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:

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