The zero product rule is a mathematical rule pertaining to algebraic formulas. The rule states that if, using the variables "a" and "b," if ab = 0 then either a or b (or both) must equal zero. This is because zero can only result from a multiplication between itself and another number. Quadratic formulas can be solved using the zero product rule through factoring and setting each side of the factor to zero, then solving.

Use the equation x^2  2x = 8 for this example. Set the entire equation equal to 0 by subtracting 8 from each side, leaving you with x^2  2x  8 = 0.

Factor x^2  2x  8 = 0. Begin the setup with an x leading each factor so that it looks like this: (x )(x ). Add in a "2" to the first grouping and a "4" to the second: (x 2)(x 4). Finish the factoring by adding the correct signs: (x + 2)(x  4). Work out the factoring to ensure that it does, indeed, equal x^2  2x  8 = 0.

Use the zero product rule to set both groups of the factor to 0: (x + 2) = 0 and (x  4) = 0. Solve each new equation for x, which will equal out to x = 2 and x = 4. Plug these solutions, one at a time, back into the original equation to confirm that they do work out correctly.