-and-(2a2b-%2B-3ab2-%E2%80%93-7ab).jpeg "(4a2b – 3ab2 + 2ab + 5) And (2a2b + 3ab2 – 7ab)")
Adding Polynomials: (4a²b – 3ab² + 2ab + 5) and (2a²b + 3ab² – 7ab)
In algebra, adding polynomials involves combining like terms. Like terms are terms that have the same variables raised to the same powers. Let's walk through the steps of adding the polynomials (4a²b – 3ab² + 2ab + 5) and (2a²b + 3ab² – 7ab):
1. Arrange the Polynomials Vertically
It's helpful to write the polynomials vertically, aligning like terms:
4a²b – 3ab² + 2ab + 5
+ 2a²b + 3ab² – 7ab
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2. Add the Coefficients of Like Terms
Add the coefficients of each like term:
- a²b terms: 4a²b + 2a²b = 6a²b
- ab² terms: -3ab² + 3ab² = 0
- ab terms: 2ab – 7ab = -5ab
- Constant terms: 5 remains unchanged.
3. Combine the Results
Combine the results to get the simplified sum:
4a²b – 3ab² + 2ab + 5
+ 2a²b + 3ab² – 7ab
----------------------
6a²b – 5ab + 5
Therefore, the sum of (4a²b – 3ab² + 2ab + 5) and (2a²b + 3ab² – 7ab) is 6a²b – 5ab + 5.