(x%2B2).jpeg "(x-5)(x+2)")
Factoring and Expanding (x-5)(x+2)
This expression represents the product of two binomials: (x-5) and (x+2). We can simplify it by using the FOIL method, which stands for First, Outer, Inner, Last.
Expanding the Expression
1. First: Multiply the first terms of each binomial:
- x * x = x²
2. Outer: Multiply the outer terms of the binomials:
- x * 2 = 2x
3. Inner: Multiply the inner terms of the binomials:
- -5 * x = -5x
4. Last: Multiply the last terms of each binomial:
- -5 * 2 = -10
Now, combine all the terms: x² + 2x - 5x - 10
Simplify by combining like terms: x² - 3x - 10
What is the factored form?
The factored form of the expression is (x-5)(x+2).
Conclusion
We have expanded the expression (x-5)(x+2) using the FOIL method and simplified it to x² - 3x - 10. We can also see that this is the factored form of the simplified expression. Understanding factoring and expanding is important for solving equations and manipulating algebraic expressions.