(x+5)(x^2+4x-8)

Jasonbradley

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Jun 17, 2024

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Expanding the Expression (x+5)(x^2+4x-8)

This article will guide you through the process of expanding the given expression: (x+5)(x^2+4x-8).

Understanding the Problem

We have two expressions:

• (x+5): This is a binomial (an expression with two terms).
• (x^2+4x-8): This is a trinomial (an expression with three terms).

Our goal is to multiply these two expressions together to obtain a simplified expression.

Using the Distributive Property

The distributive property is the key to expanding the expression. It states that multiplying a sum by a number is the same as multiplying each term of the sum by that number.

Here's how we apply it:

1. Distribute (x+5) over each term of (x^2+4x-8):

   • x(x^2+4x-8): This represents multiplying the first term of (x+5) with each term of (x^2+4x-8).
   • 5(x^2+4x-8): This represents multiplying the second term of (x+5) with each term of (x^2+4x-8).

2. Simplify each individual multiplication:

   • x(x^2+4x-8) = x^3 + 4x^2 - 8x
   • 5(x^2+4x-8) = 5x^2 + 20x - 40

3. Combine the results:

   • (x^3 + 4x^2 - 8x) + (5x^2 + 20x - 40)

4. Combine like terms:

   • x^3 + (4x^2 + 5x^2) + (-8x + 20x) - 40

5. Final simplified expression:

   • x^3 + 9x^2 + 12x - 40

Conclusion

By applying the distributive property, we successfully expanded the expression (x+5)(x^2+4x-8) to obtain the simplified form x^3 + 9x^2 + 12x - 40. This process demonstrates the importance of understanding the distributive property in algebra.