Question

Find the product. $$ \left(x+\frac{2}{3}\right)\left(x-\frac{1}{3}\right) $$

Short answer

The product is \(x^2 + \frac{1}{3}x -\frac{2}{9}\)

Step-by-step solution

Expand the Binomials

Multiply each term of the first binomial with each term of the second binomial, which will give \[ x \cdot x, x \cdot -\frac{1}{3}, \frac{2}{3} \cdot x, \frac{2}{3} \cdot -\frac{1}{3} \] .

Calculate the Multiplication

This gives \[ x^2 -\frac{1}{3}x + \frac{2}{3}x -\frac{2}{9} \] .

Combine Like Terms

Combine the terms with x, which is \(-\frac{1}{3}x + \frac{2}{3}x = \frac{1}{3}x\).

Write the Final Result

Put this together for the final result \[ x^2 + \frac{1}{3}x -\frac{2}{9} \] .