(5x+3)(x-2)

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (5x+3)(x-2)

This article will guide you through the steps of expanding the expression (5x+3)(x-2). This process is often referred to as multiplying binomials.

Understanding the Concept

When we multiply binomials, we are essentially applying the distributive property twice. The distributive property states that multiplying a sum by a number is the same as multiplying each term of the sum by that number.

Step-by-Step Solution

1. Distribute the first term of the first binomial:

   • Multiply 5x by both terms in the second binomial:
     • 5x * x = 5x²
     • 5x * -2 = -10x

2. Distribute the second term of the first binomial:

   • Multiply 3 by both terms in the second binomial:
     • 3 * x = 3x
     • 3 * -2 = -6

3. Combine the terms:

   • The expanded expression is: 5x² - 10x + 3x - 6

4. Simplify by combining like terms:

   • 5x² - 7x - 6

Final Result

Therefore, the expanded form of (5x+3)(x-2) is 5x² - 7x - 6.

Key Takeaways

• Multiplying binomials involves applying the distributive property twice.
• Each term in the first binomial must be multiplied by each term in the second binomial.
• Combine like terms after the multiplication to simplify the expression.