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Expanding the Expression (x+3)(x-7)
This article explores the process of expanding the algebraic expression (x+3)(x-7).
Understanding the Concept
The expression (x+3)(x-7) represents the product of two binomials. Expanding this expression involves applying the distributive property, often referred to as FOIL (First, Outer, Inner, Last).
Expanding using FOIL
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * -7 = -7x
- Inner: Multiply the inner terms of the binomials: 3 * x = 3x
- Last: Multiply the last terms of each binomial: 3 * -7 = -21
Now, we combine these terms:
(x+3)(x-7) = x² - 7x + 3x - 21
Finally, we simplify by combining like terms:
(x+3)(x-7) = x² - 4x - 21
Conclusion
Expanding the expression (x+3)(x-7) using the FOIL method results in the simplified form x² - 4x - 21. This process demonstrates how to multiply binomials and obtain a simplified polynomial expression.