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Expanding the Expression (x+7)(x^2-3x+2)
This article will guide you through expanding the expression (x+7)(x^2-3x+2). This involves applying the distributive property (also known as FOIL method) to simplify the expression.
Understanding the Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend separately by the number and then adding the products.
In our case, we have:
(x + 7)(x² - 3x + 2) = x(x² - 3x + 2) + 7(x² - 3x + 2)
Applying the Distributive Property
Now, let's distribute x and 7 to each term inside the parentheses:
- x(x² - 3x + 2) = x³ - 3x² + 2x
- 7(x² - 3x + 2) = 7x² - 21x + 14
Combining Like Terms
Finally, we combine the like terms to get the expanded form:
x³ - 3x² + 2x + 7x² - 21x + 14 = x³ + 4x² - 19x + 14
Conclusion
Therefore, the expanded form of (x+7)(x^2-3x+2) is x³ + 4x² - 19x + 14. This process demonstrates the power of the distributive property in simplifying algebraic expressions.