(x+9)(x+8)

2 min read Jun 17, 2024
(x+9)(x+8)

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.

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