(x%2B9)-distributive-property.jpeg "(x+2)(x+9) Distributive Property")
Using the Distributive Property to Expand (x+2)(x+9)
The distributive property is a fundamental concept in algebra that allows us to expand expressions involving multiplication. It states that for any numbers a, b, and c:
a(b + c) = ab + ac
This means that we can distribute the multiplication of 'a' to both terms inside the parentheses.
Let's apply this principle to expand the expression (x + 2)(x + 9).
Step 1: Distribute the first term
We'll begin by distributing the 'x' from the first set of parentheses to both terms in the second set:
- x(x + 9) = x * x + x * 9 = x² + 9x
Step 2: Distribute the second term
Next, we distribute the '2' from the first parentheses to the terms in the second:
- 2(x + 9) = 2 * x + 2 * 9 = 2x + 18
Step 3: Combine the results
Now, we add the results from both distributions:
- x² + 9x + 2x + 18
Step 4: Simplify
Finally, we combine the like terms:
- x² + 11x + 18
Therefore, the expanded form of (x + 2)(x + 9) using the distributive property is x² + 11x + 18.
Key Takeaway:
The distributive property is a powerful tool for simplifying expressions involving multiplication. By applying it step-by-step, we can expand complex expressions into simpler forms that are easier to manipulate and understand.