## Expanding the Expression: (x + 5)(2x - 9)

This article explores the expansion of the algebraic expression (x + 5)(2x - 9). We'll use the **FOIL** method to simplify this expression.

### Understanding the FOIL Method

**FOIL** stands for **First, Outer, Inner, Last**. This mnemonic device helps us remember the steps involved in multiplying two binomials:

**First:**Multiply the first terms of each binomial.**Outer:**Multiply the outer terms of the binomials.**Inner:**Multiply the inner terms of the binomials.**Last:**Multiply the last terms of each binomial.

### Applying FOIL to (x + 5)(2x - 9)

Let's apply the FOIL method to our expression:

**First:**(x)(2x) = 2x²**Outer:**(x)(-9) = -9x**Inner:**(5)(2x) = 10x**Last:**(5)(-9) = -45

Now, we combine the resulting terms:

2x² - 9x + 10x - 45

Finally, we simplify by combining like terms:

**2x² + x - 45**

### Conclusion

By using the FOIL method, we successfully expanded the expression (x + 5)(2x - 9) to **2x² + x - 45**. This technique provides a systematic approach for multiplying binomials and obtaining a simplified polynomial expression.