Question

Find the product. $$ \left(x+\frac{1}{8}\right)\left(x-\frac{9}{8}\right) $$

Short answer

The product of \(x + \frac{1}{8}\) and \(x - \frac{9}{8}\) is \(x^2 - x - \frac{9}{64}\).

Step-by-step solution

Apply the FOIL method

The FOIL method stands for First, Outer, Inner, and Last. It is a method for multiplying binomials. First, the first terms of each binomial are multiplied. Then, the outer terms are multiplied. After that, the inner terms are multiplied. Finally, the last terms are multiplied. So, according to the FOIL method, the product of \(x + \frac{1}{8}\) and \(x - \frac{9}{8}\) can be expanded like: \(x * x + x * -\frac{9}{8} + \frac{1}{8} * x + \frac{1}{8} * -\frac{9}{8}\).

Simplify each term

The next step is to simplify each term of the multiplication. \(x * x = x^2\), \(x * -\frac{9}{8} = -\frac{9}{8}x\), \(\frac{1}{8} * x = \frac{1}{8}x\), and \(\frac{1}{8} * -\frac{9}{8} = -\frac{9}{64}\). Putting all these terms together, the expression becomes: \(x^2 -\frac{9}{8}x +\frac{1}{8}x - \frac{9}{64}\).

Combine like terms

In the final step, combine like terms. The terms \(-\frac{9}{8}x\) and \(\frac{1}{8}x\) can be combined because they are like terms. Adding \(-\frac{9}{8}x + \frac{1}{8}x\) equals to \(-\frac{8}{8}x = -x\). So, the final expression becomes: \(x^2 - x - \frac{9}{64}\).