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Expanding the Expression (2x + 5)(x + 3)
This article will guide you through expanding the expression (2x + 5)(x + 3). This involves applying the distributive property (also known as the FOIL method).
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 simpler terms, it involves multiplying each term in the first set of parentheses by each term in the second set of parentheses.
Expanding the Expression
- Multiply the first terms of each binomial: (2x) * (x) = 2x²
- Multiply the outer terms: (2x) * (3) = 6x
- Multiply the inner terms: (5) * (x) = 5x
- Multiply the last terms of each binomial: (5) * (3) = 15
Combining the Terms
Now, combine the terms you've obtained:
2x² + 6x + 5x + 15
Finally, simplify by combining the like terms:
2x² + 11x + 15
Conclusion
Therefore, the expanded form of the expression (2x + 5)(x + 3) is 2x² + 11x + 15. This process demonstrates the power of the distributive property in simplifying and manipulating algebraic expressions.