Converting Factored Form to Standard Form

Quadratic equations in the factored form can be converted to the standard format simply. If we take an example of the equation to show the process.

$$y=(x+4)(x+3)$$

Using a process called FOIL, standing for first, outside, inside, last. This describes the order in which the components of each bracket are multiplied in (Figure 1a). Alternatively, you can think of this in terms of a table (Figure 1b), which is a way I prefer to visualize it.

Diagrams showing how to conduct the FOIL proceedure to convert a quadratic expression in the factored form into an expression in the standard form — Figure 1: Multiplying the terms contained in each bracket by one another using the FOIL method, by multiplying the First terms in the brackets, the Outisde terms, the Inside terms, and the Last terms. This can also be shown in the table form.

Whichever way is used, you will finish off with a selection of terms that can be combined into a single expression.

$$y=x^2+3x+4x+12$$

Some of these terms (the $3x$ and $4x$ terms) can be combined, as they are like terms. Thus giving the quadratic equation in the standard form.

$$y=x^2+7x+12$$

This then completes the quadratic equation in the standard form.