Step 1: Expand the Expression
To simplify the expression (a+b)(2a-3b+c)-(2a-3b)c, we first need to expand the first part.
- Expand (a+b)(2a-3b+c):
- Multiply each term in (a+b) by each term in (2a-3b+c):
- a * 2a = 2a^2
- a * (-3b) = -3ab
- a * c = ac
- b * 2a = 2ab
- b * (-3b) = -3b^2
- b * c = bc
- Combine the results:
- 2a^2 + (-3ab + 2ab) + ac - 3b^2 + bc
- This simplifies to 2a^2 - ab + ac - 3b^2 + bc
Step 2: Expand the Second Part
Now we need to expand the second part of the expression.
- Expand (2a-3b)c:
- Multiply each term in (2a-3b) by c:
- 2a * c = 2ac
- -3b * c = -3bc
- Combine the results:
- This gives us 2ac - 3bc.
Step 3: Combine Both Parts
Now we can combine the results from both expansions:
- Combine: (2a^2 - ab + ac - 3b^2 + bc) - (2ac - 3bc)
This leads to:
- Combine like terms:
- 2a^2 - ab + ac - 2ac - 3b^2 + bc + 3bc
- Which simplifies to: 2a^2 - ab - ac - 3b^2 + 4bc
Final Result
The simplified expression is:
2a^2 - ab - ac - 3b^2 + 4bc