(x%2B9).jpeg "(x+7)(x+9)")
Expanding (x+7)(x+9)
This expression represents the product of two binomials: (x+7) and (x+9). To expand it, we can use the FOIL method:
First: Multiply the first terms of each binomial. Outer: Multiply the outer terms of the binomials. Inner: Multiply the inner terms of the binomials. Last: Multiply the last terms of each binomial.
Let's apply this to our expression:
F: x * x = x² O: x * 9 = 9x I: 7 * x = 7x L: 7 * 9 = 63
Now, we add all the terms together:
x² + 9x + 7x + 63
Finally, we combine the like terms:
x² + 16x + 63
Therefore, the expanded form of (x+7)(x+9) is x² + 16x + 63.
Understanding the Concept
Expanding expressions like this is fundamental in algebra. It allows us to simplify complex expressions and solve equations. Here's why it's important:
- Factoring: Knowing how to expand can help you factor expressions in reverse. This is useful for solving equations.
- Understanding Quadratic Equations: The expanded form, x² + 16x + 63, represents a quadratic equation. We can use this to find solutions and graph the equation.
- Applications in Real-World Problems: Quadratic equations are used in various fields, including physics, engineering, and finance.
By mastering this basic skill, you lay the foundation for deeper understanding and problem-solving in algebra and beyond.