## 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.