(a + 3)(a - 2)

Jasonbradley

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Jun 16, 2024

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Expanding the Expression: (a + 3)(a - 2)

This article will guide you through expanding the expression (a + 3)(a - 2). This is a fundamental concept in algebra and involves using the distributive property.

The Distributive Property

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

We can apply this to our expression:

Step 1: Expand the first term (a + 3)

• Multiply a by each term inside the second parentheses:

  • a * a = a²
  • a * -2 = -2a

• Multiply 3 by each term inside the second parentheses:

  • 3 * a = 3a
  • 3 * -2 = -6

Step 2: Combine the terms

Now we have: a² - 2a + 3a - 6

Step 3: Simplify

Combine the like terms (-2a + 3a): a² + a - 6

Final Result

Therefore, the expanded form of (a + 3)(a - 2) is a² + a - 6.

Key Takeaways

• The distributive property is crucial for expanding expressions.
• It involves multiplying each term in one factor by each term in the other factor.
• Remember to combine like terms after expanding.

By understanding the distributive property and applying it to specific expressions, you can confidently simplify and solve algebraic problems.