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Expanding the Expression (2x-3)(x+5)
This article will guide you through the process of expanding the expression (2x-3)(x+5).
Understanding the Problem
The expression (2x-3)(x+5) represents the product of two binomials. To expand it, we need to distribute each term in the first binomial with each term in the second binomial.
Applying the Distributive Property
The distributive property states that a(b + c) = ab + ac. We can apply this property to our expression:
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Step 1: Distribute the 2x: 2x(x + 5) = 2x² + 10x
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Step 2: Distribute the -3: -3(x + 5) = -3x - 15
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Step 3: Combine the results from step 1 and step 2: (2x² + 10x) + (-3x - 15) = 2x² + 7x - 15
Final Answer
Therefore, the expanded form of (2x-3)(x+5) is 2x² + 7x - 15.
Additional Notes
- Expanding binomials is a fundamental skill in algebra.
- You can check your answer by substituting a value for x into both the original and expanded expressions. The results should be equal.
- Remember to simplify your expression by combining like terms.