There is a general way of writing every quantity or relation or expression in mathematics which can be defined as the standard form. Let’s consider an example of a number which can be written simply in its standard form, say 6444. This number can further be written in an expanded form as (6 * 1000) + (4 *100) + (4 * 10) + (4 * 1). This is representation of Numbers in ones, tens, hundreds, thousands and so on. There are certain operations which have to be performed in a specific order to know how to do standard form.
As per the above example considered first we perform the multiplication operation, because before addition we always go for multiplication. In example, 6 * 1000 equals 6,000; 4 * 100 equals 400; 4 * 10 equals 40; and 4 times 1 equals 4. The equation is now given as 6,000 + 400 + 40 + 4. Adding up these multiplication results to get the original standard number as: 6,000 + 400 + 40 + 4 equals 6444.
Like this we can have many such standard forms related to numbers, equations, expressions, functions etc. Let’s consider another example of finding Linear Equations in a standard form. Linear equations allow plotting the variables graphically when solved. In general the linear equations that we consider consists of two unsolved variables, with a usual representation of them by 'x' and 'y' respectively. The standard form of a linear equation can be given as: ax + by = c. In this equation a, b, c are the constants, with 'a' and 'b' as coefficients of 'x' and 'y' respectively.
Say for example we have a linear equation: 20y + 12 = 4x is written as by + c = ax. Writing it in standard form as: 20y + -4x + 12 = 0, where a = 20, b = -4 and c = 12.
In this way we can write standard forms for various other mathematical forms.