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Expanding (x + 8)(x + 2)
In mathematics, expanding expressions involves multiplying terms to simplify them. Here, we'll explore how to expand the expression (x + 8)(x + 2).
Using the FOIL Method
The FOIL method is a common technique used for expanding binomials (expressions with two terms). FOIL stands for First, Outer, Inner, Last:
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * 2 = 2x
- Inner: Multiply the inner terms of the binomials: 8 * x = 8x
- Last: Multiply the last terms of each binomial: 8 * 2 = 16
Combining these results, we get:
(x + 8)(x + 2) = x² + 2x + 8x + 16
Simplifying the Expression
The final step is to combine the like terms:
x² + 2x + 8x + 16 = x² + 10x + 16
Therefore, the expanded form of (x + 8)(x + 2) is x² + 10x + 16.
Other Methods
While the FOIL method is widely used, there are other ways to expand binomials:
- Distributive Property: You can apply the distributive property twice, distributing each term in the first binomial over the second binomial.
- Tabular Method: A visual method using a table to organize the multiplications.
Conclusion
Expanding expressions like (x + 8)(x + 2) is a fundamental skill in algebra. Understanding the FOIL method or other techniques allows you to simplify these expressions and further manipulate them in equations and other mathematical contexts.