Question

Rewrite in simplest terms: minus, 0, point, 3, left parenthesis, minus, 5, a, plus, 3, b, right parenthesis, plus, 9, b, minus, 0, point, 9, left parenthesis, 7, b, plus, 8, a, right parenthesis−0.3(−5a+3b)+9b−0.9(7b+8a)

Answer 1

To simplify the expression \(-0.3(-5a + 3b) + 9b - 0.9(7b + 8a)\), let's distribute the coefficients and combine like terms step by step.

1. Distribute \(-0.3\) to \(-5a + 3b\):
\[
-0.3 \times -5a = 1.5a
\]
\[
-0.3 \times 3b = -0.9b
\]
So, \(-0.3(-5a + 3b) = 1.5a - 0.9b\).

2. Distribute \(-0.9\) to \(7b + 8a\):
\[
-0.9 \times 7b = -6.3b
\]
\[
-0.9 \times 8a = -7.2a
\]
Thus, \(-0.9(7b + 8a) = -7.2a - 6.3b\).

3. Now, combine all the parts:
\[
1.5a - 0.9b + 9b - 7.2a - 6.3b
\]

4. Combine like terms for \(a\):
\[
1.5a - 7.2a = -5.7a
\]

5. Combine like terms for \(b\):
\[
-0.9b + 9b - 6.3b = 1.8b
\]

So, putting it all together, the simplified expression is:
\[
-5.7a + 1.8b
\]