## Understanding (b - 7)<sup>2</sup>

(b - 7)<sup>2</sup> is a mathematical expression that represents the square of the difference between a variable 'b' and the constant 7. Let's break down what this means and how to expand it:

### What Does Squaring Mean?

Squaring a number means multiplying it by itself. So, (b - 7)<sup>2</sup> is equivalent to:

**(b - 7) * (b - 7)**

### Expanding the Expression

To expand the expression, we need to use the **FOIL** method (First, Outer, Inner, Last) for multiplying binomials:

**First:**Multiply the first terms of each binomial:**b * b = b<sup>2</sup>****Outer:**Multiply the outer terms of each binomial:**b * -7 = -7b****Inner:**Multiply the inner terms of each binomial:**-7 * b = -7b****Last:**Multiply the last terms of each binomial:**-7 * -7 = 49**

Now, combine the terms:

**b<sup>2</sup> - 7b - 7b + 49**

Finally, simplify by combining the like terms:

**b<sup>2</sup> - 14b + 49**

### Conclusion

Therefore, the expanded form of (b - 7)<sup>2</sup> is **b<sup>2</sup> - 14b + 49**. This expression can be useful in various mathematical contexts, including solving equations, simplifying expressions, and understanding the relationship between variables.