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)

To simplify the expression \( -0.3(-5a + 3b) + 9b - 0.9(7b + 8a) \), we can use the distributive property and combine like terms. Let's go through the steps:

1. **Distribute \( -0.3 \) in the first set of parentheses:**
   \[
   -0.3 \cdot (-5a) + (-0.3 \cdot 3b) = 1.5a - 0.9b
   \]

2. **Distribute \( -0.9 \) in the second set of parentheses:**
   \[
   -0.9 \cdot 7b + (-0.9 \cdot 8a) = -6.3b - 7.2a
   \]

3. **Combine all the terms from steps 1 and 2 along with \( 9b \):**
   \[
   1.5a - 0.9b + 9b - 6.3b - 7.2a
   \]

4. **Combine like terms (terms with \( a \) and terms with \( b \)):**

   - For \( a \) terms: \( 1.5a - 7.2a = -5.7a \)
   - For \( b \) terms: \( -0.9b + 9b - 6.3b = 1.8b \)

Therefore, the simplified form of the expression is:

\[
-5.7a + 1.8b
\]

Would you like further details or have any questions?

Here are five related questions to expand your understanding:

1. How would you simplify \( 0.5(-4x + 6y) - 1.2(5x + 2y) \)?
2. What is the importance of the distributive property in algebra?
3. How can you check your simplified expression to ensure it's correct?
4. Can you explain how to combine decimal coefficients in algebraic expressions?
5. What is the effect of a negative sign outside parentheses on the terms inside?

**Tip:** When dealing with negative signs and decimal coefficients, be careful to distribute correctly to avoid mistakes in sign and value.

Learn how to simplify the expression -0.3(-5a + 3b) + 9b - 0.9(7b + 8a) step-by-step. This problem involves using the distributive property and combining like terms in algebra. Suitable for high school students.

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