(5x%2B1)%3D(x%5E2)(5x)%2B(x%5E2)(1)%2B(-2)(5x)%2B(-2)(1)-is-an-example-of.jpeg "(x^2-2)(5x+1)=(x^2)(5x)+(x^2)(1)+(-2)(5x)+(-2)(1) Is An Example Of")
The Distributive Property in Action
The equation (x^2-2)(5x+1) = (x^2)(5x) + (x^2)(1) + (-2)(5x) + (-2)(1) is a clear example of the distributive property.
What is the Distributive Property?
The distributive property is a fundamental rule in algebra that states:
For any numbers a, b, and c: a(b + c) = ab + ac
This means that when you multiply a number (a) by a sum (b + c), you can distribute the multiplication to each term inside the parentheses.
Breaking Down the Example
In the given equation:
- (x^2-2) is the number (a) being multiplied.
- (5x+1) is the sum (b + c).
By applying the distributive property:
- (x^2)(5x) = the product of the first term in the first set of parentheses and the first term in the second set of parentheses.
- (x^2)(1) = the product of the first term in the first set of parentheses and the second term in the second set of parentheses.
- (-2)(5x) = the product of the second term in the first set of parentheses and the first term in the second set of parentheses.
- (-2)(1) = the product of the second term in the first set of parentheses and the second term in the second set of parentheses.
The Power of the Distributive Property
The distributive property is essential for simplifying and solving algebraic expressions. It allows us to:
- Expand and simplify expressions: As seen in the example, the distributive property helps break down complex expressions into simpler terms.
- Solve equations: By applying the distributive property, we can isolate variables and solve for their values.
- Factor expressions: The distributive property also helps in reversing the process of expanding, enabling us to factor expressions into simpler forms.
Understanding and applying the distributive property is crucial for mastering basic algebra and tackling more complex mathematical concepts.