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.