(x-9)^2 Expand

2 min read Jun 17, 2024

Expanding (x - 9)²

In algebra, expanding a squared binomial like (x - 9)² involves multiplying the binomial by itself. Here's how to do it:

Understanding the Concept

The expression (x - 9)² is equivalent to (x - 9) * (x - 9). To expand it, we need to apply the distributive property (also known as FOIL method).

The FOIL Method

FOIL stands for First, Outer, Inner, Last. It's a helpful mnemonic for remembering the steps in expanding a binomial multiplied by another binomial.

First: Multiply the first terms of each binomial: x * x = x²
Outer: Multiply the outer terms of the binomials: x * -9 = -9x
Inner: Multiply the inner terms of the binomials: -9 * x = -9x
Last: Multiply the last terms of each binomial: -9 * -9 = 81

Combining Like Terms

Now we have: x² - 9x - 9x + 81

Combining the like terms (-9x - 9x), we get:

x² - 18x + 81

Final Result

Therefore, the expanded form of (x - 9)² is x² - 18x + 81.

Key Takeaways

Expanding a squared binomial involves multiplying it by itself.
The FOIL method helps to ensure all terms are multiplied correctly.
Remember to combine like terms for the final simplified expression.