(2x%2B5)-(x%2By)(x%2B3).jpeg "(x+y)(2x+5)-(x+y)(x+3)")
Factoring and Simplifying the Expression: (x+y)(2x+5)-(x+y)(x+3)
This expression involves factoring and simplifying. Let's break it down step-by-step.
1. Identifying Common Factors
Notice that both terms in the expression have a common factor of (x+y). This is crucial for simplifying.
2. Factoring out the Common Factor
We can rewrite the expression as: (x+y)(2x+5) - (x+y)(x+3) = (x+y)[(2x+5)-(x+3)]
3. Simplifying the Remaining Expression
Now we simplify the expression inside the square brackets: (x+y)[(2x+5)-(x+3)] = (x+y)(2x + 5 - x - 3)
Combining like terms: (x+y)(2x + 5 - x - 3) = (x+y)(x + 2)
Final Result
Therefore, the simplified form of the expression (x+y)(2x+5)-(x+y)(x+3) is (x+y)(x+2).
Importance of Factoring
Factoring is a powerful tool in algebra. It allows us to:
- Simplify expressions: As we saw, factoring can make complex expressions much easier to work with.
- Solve equations: Factoring is essential for solving many types of equations, particularly quadratic equations.
- Analyze functions: Factoring can help us understand the behavior of functions and identify important features like roots and intercepts.
By mastering factoring techniques, you can unlock a deeper understanding of algebraic concepts and solve a wide range of problems.