## Expanding the Expression (x+3)(x-7)

This article explores the process of expanding the algebraic expression **(x+3)(x-7)**.

### Understanding the Concept

The expression (x+3)(x-7) represents the product of two binomials. Expanding this expression involves applying the distributive property, often referred to as **FOIL** (First, Outer, Inner, Last).

### Expanding using FOIL

**First:**Multiply the first terms of each binomial:**x * x = x²****Outer:**Multiply the outer terms of the binomials:**x * -7 = -7x****Inner:**Multiply the inner terms of the binomials:**3 * x = 3x****Last:**Multiply the last terms of each binomial:**3 * -7 = -21**

Now, we combine these terms:

**(x+3)(x-7) = x² - 7x + 3x - 21**

Finally, we simplify by combining like terms:

**(x+3)(x-7) = x² - 4x - 21**

### Conclusion

Expanding the expression (x+3)(x-7) using the FOIL method results in the simplified form **x² - 4x - 21**. This process demonstrates how to multiply binomials and obtain a simplified polynomial expression.