## Expanding the Expression: (x+4)(x+7)

This article will walk you through the steps involved in expanding the expression **(x+4)(x+7)**. This process is fundamental in algebra and helps us understand how to manipulate and simplify expressions.

### The FOIL Method

The **FOIL** method provides a systematic way to expand expressions of this form. FOIL stands for:

**F**irst: Multiply the first terms of each binomial.**O**uter: Multiply the outer terms of the binomials.**I**nner: Multiply the inner terms of the binomials.**L**ast: Multiply the last terms of each binomial.

Let's apply FOIL to our expression:

**First:**(x) * (x) =**x²****Outer:**(x) * (7) =**7x****Inner:**(4) * (x) =**4x****Last:**(4) * (7) =**28**

Now we combine the terms:

x² + 7x + 4x + 28

### Simplifying the Expression

Finally, we simplify by combining the like terms (the terms with 'x'):

**x² + 11x + 28**

### Conclusion

Therefore, the expanded form of (x+4)(x+7) is **x² + 11x + 28**. Understanding how to expand binomials like this is crucial for solving algebraic equations and understanding various mathematical concepts.