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Expanding the Expression (x + 8)(x + 3)
This article explores how to expand the expression (x + 8)(x + 3). This is a common problem in algebra, and understanding how to solve it is essential for further mathematical exploration.
The FOIL Method
The most common method for expanding expressions of this form is the FOIL method. FOIL stands for:
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * 3 = 3x
- Inner: Multiply the inner terms of the binomials: 8 * x = 8x
- Last: Multiply the last terms of each binomial: 8 * 3 = 24
Expanding the Expression
Using the FOIL method, we get:
(x + 8)(x + 3) = x² + 3x + 8x + 24
Simplifying the Expression
Finally, we can simplify the expression by combining like terms:
x² + 3x + 8x + 24 = x² + 11x + 24
Conclusion
Therefore, the expanded and simplified form of the expression (x + 8)(x + 3) is x² + 11x + 24. Understanding the FOIL method is crucial for expanding and simplifying expressions in algebra.