## Expanding (7a-1)^2

The expression (7a-1)^2 represents the square of the binomial (7a-1). To expand this expression, we can use the **FOIL method** or the **square of a binomial formula**.

### Expanding using FOIL

**FOIL** stands for **First, Outer, Inner, Last**. It's a method for multiplying two binomials. Here's how it applies to our expression:

**First:**Multiply the first terms of each binomial: (7a) * (7a) =**49a^2****Outer:**Multiply the outer terms: (7a) * (-1) =**-7a****Inner:**Multiply the inner terms: (-1) * (7a) =**-7a****Last:**Multiply the last terms: (-1) * (-1) =**1**

Now, add all the terms together: 49a^2 - 7a - 7a + 1

Finally, combine the like terms: **49a^2 - 14a + 1**

### Expanding using the square of a binomial formula

The square of a binomial formula states: (a + b)^2 = a^2 + 2ab + b^2

Applying this to our expression:

- Identify 'a' and 'b': a = 7a and b = -1
- Substitute the values into the formula: (7a)^2 + 2 (7a) (-1) + (-1)^2
- Simplify:
**49a^2 - 14a + 1**

### Conclusion

Both methods lead to the same expanded form of (7a-1)^2, which is **49a^2 - 14a + 1**. Remember, the FOIL method is helpful for expanding any two binomials, while the square of a binomial formula is specifically useful for squaring binomials.