(x-5)(x+2)

2 min read Jun 17, 2024
(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.

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