(x+3)(x−5)

Jasonbradley

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Jun 16, 2024

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Expanding (x+3)(x-5)

In algebra, expanding expressions involves simplifying them by removing parentheses and applying the distributive property. Let's look at how to expand the expression (x+3)(x-5).

Understanding the Distributive Property

The distributive property states that for any numbers a, b, and c: a(b + c) = ab + ac

This means we multiply the term outside the parentheses by each term inside the parentheses.

Applying the Distributive Property

1. Multiply the first term of the first parenthesis (x) by each term in the second parenthesis:

   • x * x = x²
   • x * -5 = -5x

2. Multiply the second term of the first parenthesis (3) by each term in the second parenthesis:

   • 3 * x = 3x
   • 3 * -5 = -15

3. Combine the resulting terms:

   • x² - 5x + 3x - 15

4. Simplify by combining like terms:

   • x² - 2x - 15

Conclusion

Therefore, the expanded form of (x+3)(x-5) is x² - 2x - 15. This process can be applied to expand any expression with multiple factors using the distributive property.