5a-4b + 2 (-a + 2b) -9a +12b
5a-4b-2a+4b-9a+12b
5a-2a-9a-4b+4b+12b
5a-11a-4b+16b
-6a+12b
12b-6a
To simplify the expression 5a - 4b + 2(-a + 2b) - 9a + 12b, we can use the distributive property to multiply the coefficients with the terms inside the parentheses. Let's break it down step by step:
1. Start with the given expression: 5a - 4b + 2(-a + 2b) - 9a + 12b.
2. Distribute the 2 to the terms inside the parentheses: 5a - 4b + 2(-a) + 2(2b) - 9a + 12b.
3. Simplify the multiplication: 5a - 4b - 2a + 4b - 9a + 12b.
4. Combine like terms. Group the terms with the same variables together: (5a - 2a - 9a) + (-4b + 4b + 12b).
5. Simplify each group separately:
- The group with 'a' terms: (5a - 2a - 9a) simplifies to -6a.
- The group with 'b' terms: (-4b + 4b + 12b) simplifies to 12b.
6. Combine the simplified groups: -6a + 12b.
Therefore, the simplified expression for 5a - 4b + 2(-a + 2b) - 9a + 12b is -6a + 12b.