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Expanding the Expression: (x - 5)(2x + 3)
This article explores the expansion of the expression (x - 5)(2x + 3) using the distributive property.
Understanding the Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.
In mathematical terms, this is represented as: a(b + c) = ab + ac
Applying the Distributive Property
To expand the expression (x - 5)(2x + 3), we apply the distributive property twice:
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First Distribution: We multiply the first term of the first binomial (x) by each term of the second binomial (2x + 3): x(2x + 3) = 2x² + 3x
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Second Distribution: We multiply the second term of the first binomial (-5) by each term of the second binomial (2x + 3): -5(2x + 3) = -10x - 15
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Combining the Results: We add the results of the two distributions: (2x² + 3x) + (-10x - 15)
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Simplifying: Finally, we combine like terms: 2x² - 7x - 15
Conclusion
Therefore, the expanded form of the expression (x - 5)(2x + 3) is 2x² - 7x - 15. This process demonstrates the application of the distributive property to expand expressions involving binomials.