%5E2-answer.jpeg "(x+9)^2 Answer")
Expanding (x + 9)²: A Step-by-Step Guide
Understanding how to expand expressions like (x + 9)² is fundamental in algebra. This expression represents the square of a binomial, which means multiplying it by itself. Here's a breakdown of the process:
Understanding the Concept
(x + 9)² is equivalent to (x + 9) * (x + 9). To expand this, we need to distribute each term in the first set of parentheses across the second set.
The FOIL Method
A helpful mnemonic for expanding binomials is FOIL:
- First: Multiply the first terms of each binomial (x * x)
- Outer: Multiply the outer terms of the binomials (x * 9)
- Inner: Multiply the inner terms of the binomials (9 * x)
- Last: Multiply the last terms of each binomial (9 * 9)
Applying the FOIL Method
- First: x * x = x²
- Outer: x * 9 = 9x
- Inner: 9 * x = 9x
- Last: 9 * 9 = 81
Combining Like Terms
Now we have: x² + 9x + 9x + 81
Combining the like terms (9x + 9x), the final expanded form is:
x² + 18x + 81
Conclusion
Therefore, the expanded form of (x + 9)² is x² + 18x + 81. Remember, this process of expanding binomials is a crucial skill in algebra and is used extensively in solving various equations and simplifying expressions.