(x%2B5)-distributive-property.jpeg "(x+2)(x+5) Distributive Property")
Understanding the Distributive Property: (x + 2)(x + 5)
The distributive property is a fundamental concept in algebra that allows us to simplify expressions involving multiplication. It states that multiplying a sum by a number is the same as multiplying each addend by that number and then adding the products.
In this article, we will explore how to apply the distributive property to expand the expression (x + 2)(x + 5).
Step-by-Step Expansion
- Identify the terms: We have two binomials, (x + 2) and (x + 5), being multiplied.
- Multiply the first term of the first binomial by each term in the second binomial:
- x * x = x²
- x * 5 = 5x
- Multiply the second term of the first binomial by each term in the second binomial:
- 2 * x = 2x
- 2 * 5 = 10
- Combine the results: We have the following terms: x², 5x, 2x, and 10
- Simplify by combining like terms: x² + 5x + 2x + 10 = x² + 7x + 10
Visual Representation
The distributive property can be visualized using the FOIL method (First, Outer, Inner, Last):
- First: x * x = x²
- Outer: x * 5 = 5x
- Inner: 2 * x = 2x
- Last: 2 * 5 = 10
This method helps us remember to multiply each term in the first binomial by each term in the second binomial.
Conclusion
By applying the distributive property, we successfully expanded the expression (x + 2)(x + 5) into x² + 7x + 10. This demonstrates the power and simplicity of the distributive property in simplifying algebraic expressions. Understanding and applying this property is essential for further exploration of algebra and higher level mathematics.