## Factoring and Expanding (x - 8)(x - 7)

This expression represents the product of two binomials: (x - 8) and (x - 7). We can approach this in two ways:

### Expanding the Expression

To expand this, we use the **FOIL** method:

**F**irst: Multiply the first terms of each binomial: x * x = x²**O**uter: Multiply the outer terms of the binomials: x * -7 = -7x**I**nner: Multiply the inner terms of the binomials: -8 * x = -8x**L**ast: Multiply the last terms of each binomial: -8 * -7 = 56

Now we combine the terms:

x² - 7x - 8x + 56 = **x² - 15x + 56**

### Factoring the Expression

If we are given the expanded form, x² - 15x + 56, we can factor it back into the original binomials. Here's how:

**Find two numbers that multiply to 56 and add up to -15.**- In this case, the numbers are -8 and -7.

**Rewrite the middle term (-15x) using these two numbers:**x² - 8x - 7x + 56**Group the terms:**(x² - 8x) + (-7x + 56)**Factor out the greatest common factor from each group:**x(x - 8) - 7(x - 8)**Factor out the common binomial (x - 8):**(x - 8)(x - 7)

**Therefore, the factored form of x² - 15x + 56 is (x - 8)(x - 7).**

These processes, expanding and factoring, are essential in algebra and provide valuable tools for solving equations and simplifying expressions.