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Expanding and Simplifying (x + 9)(x + 8)
This expression represents the product of two binomials: (x + 9) and (x + 8). To expand and simplify 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 * 8 = 8x
- I: 9 * x = 9x
- L: 9 * 8 = 72
Now, we combine the terms:
x² + 8x + 9x + 72
Finally, we simplify by combining like terms:
x² + 17x + 72
Therefore, the expanded and simplified form of (x + 9)(x + 8) is x² + 17x + 72.
Understanding the Result
The expression x² + 17x + 72 represents a quadratic equation. It can be used to model various real-world scenarios involving relationships that involve a squared term.
For example:
- It can represent the area of a rectangle with sides of length (x + 9) and (x + 8).
- It can describe the trajectory of a projectile thrown into the air.
By understanding how to expand and simplify expressions like (x + 9)(x + 8), we gain valuable insights into quadratic relationships and their applications in various fields.