## Expanding (-5+v)<sup>2</sup>

This expression represents the square of a binomial, specifically the sum of -5 and the variable *v*. To expand it, we can apply the **FOIL method** or use the **square of a binomial formula**.

### Using the FOIL Method

FOIL stands for **First, Outer, Inner, Last**, and it helps us multiply two binomials:

**First:**Multiply the first terms of each binomial: (-5) * (-5) = 25**Outer:**Multiply the outer terms of the binomials: (-5) * v = -5v**Inner:**Multiply the inner terms of the binomials: v * (-5) = -5v**Last:**Multiply the last terms of each binomial: v * v = v<sup>2</sup>

Now, add all the terms together: 25 - 5v - 5v + v<sup>2</sup>

Finally, combine the like terms: **v<sup>2</sup> - 10v + 25**

### Using the Square of a Binomial Formula

The square of a binomial formula is: (a + b)<sup>2</sup> = a<sup>2</sup> + 2ab + b<sup>2</sup>

In our case, a = -5 and b = v. Applying the formula:

(-5 + v)<sup>2</sup> = (-5)<sup>2</sup> + 2(-5)(v) + v<sup>2</sup>

Simplifying: **v<sup>2</sup> - 10v + 25**

### Conclusion

Both methods lead to the same expanded expression: **v<sup>2</sup> - 10v + 25**.

This demonstrates the versatility of applying different mathematical tools to solve the same problem.