## Expanding the Expression (6x + 1)(1 - 3x)

This article will explore the expansion of the expression **(6x + 1)(1 - 3x)**. We will utilize the **FOIL** method, which stands for **First, Outer, Inner, Last**, to simplify the expression.

### The FOIL Method

The FOIL method is a helpful mnemonic for remembering how to multiply two binomials. It provides a systematic way to multiply each term in the first binomial by each term in the second binomial:

**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.

### Expanding the Expression

Let's apply the FOIL method to our expression (6x + 1)(1 - 3x):

**First:**(6x) * (1) =**6x****Outer:**(6x) * (-3x) =**-18x²****Inner:**(1) * (1) =**1****Last:**(1) * (-3x) =**-3x**

Now, we combine all the terms: 6x - 18x² + 1 - 3x

Finally, we arrange the terms in descending order of their exponents:

**-18x² + 3x + 1**

Therefore, the expanded form of the expression (6x + 1)(1 - 3x) is **-18x² + 3x + 1**.

### Conclusion

Using the FOIL method, we successfully expanded the expression (6x + 1)(1 - 3x) into its simplified form, -18x² + 3x + 1. This method provides a straightforward approach to multiplying binomials and understanding the resulting polynomial.