Previously, you learned how to expand a quadratic expression in factored form and write it in standard form by applying the distributive property.

For example, to expand , we apply the distributive property to multiply  by  and 4 by . Then, we apply the property again to multiply by ,  by 5, 4 by , and 4 by 5. 

The diagram helps us see that is equivalent to , or in standard form, .

• The linear term, or the term with a single factor of  in the standard form of a quadratic expression, is and has a coefficient of 9, which is the sum of 5 and 4.
• The constant term, 20, is the product of 5 and 4.

We can use these observations to reason in the other direction: starting with an expression in standard form and writing it in factored form.

For example, suppose we wish to write in factored form.