(x%2B10)-identity.jpeg "(x+4)(x+10) Identity")
Understanding the Identity: (x + 4)(x + 10)
The expression (x + 4)(x + 10) represents the product of two binomials. It's a common algebraic expression that can be simplified using the FOIL method.
FOIL stands for First, Outer, Inner, Last, and it helps us multiply two binomials systematically:
- First: Multiply the first terms of each binomial: x * x = x²
- Outer: Multiply the outer terms of the binomials: x * 10 = 10x
- Inner: Multiply the inner terms of the binomials: 4 * x = 4x
- Last: Multiply the last terms of each binomial: 4 * 10 = 40
Adding all these terms together, we get:
(x + 4)(x + 10) = x² + 10x + 4x + 40
Simplifying by combining the like terms (10x and 4x), we get the final expanded form:
(x + 4)(x + 10) = x² + 14x + 40
Key Takeaways:
- The expression (x + 4)(x + 10) represents the product of two binomials.
- Using the FOIL method, we can expand the expression and obtain a quadratic equation.
- The expanded form of (x + 4)(x + 10) is x² + 14x + 40.
Applications:
This identity can be applied in various mathematical contexts, including:
- Solving quadratic equations: When the quadratic equation is factored into the form (x + 4)(x + 10), we can easily find its roots.
- Graphing quadratic functions: Understanding the factored form can help us identify the vertex and intercepts of the parabola represented by the quadratic function.
- Algebraic manipulations: This identity can be used to simplify complex expressions and solve algebraic equations.
This understanding of the identity (x + 4)(x + 10) provides a foundation for solving a wide range of algebraic problems.