This type of expression is very useful when you are working with operations and formulas. The squared operation is represented by (x²). When given a value for x, you plug in that value in the place of x, and perform the operation. Given x = 2, for example, x² = 4. If you are looking to buy carpeting, the area formula: l x w (length times width) allows you to plug in the dimensions of a room to determine the amount of carpeting needed.
When simplifying a variable expression, there is an order for applying operations that must be observed. Any elements (numbers, variables or combination thereof) within a set of parentheses, or other group-forming symbols, such as absolute value markers | |, must be simplified first; followed by any elements with exponents (3² = 9), or square roots (√x² = x). Then any multiplication or division is performed, in left-to-right order, followed by addition and subtraction, in the same order. Failure to observe the order of operations results in incorrect solutions.
Given the expression: x (3x² + 7) + 4x/12, first we can simplify, then solve for a given value of variable x. Since there is no simplification possible within the parentheses, we simplify the first part by multiplying through: x (3x² + 7) = 3x³ + 7x. The second part of the expression can be simplified by multiplying through by 1/4: (4x(1/4)) / (12(1/4)) = x/3. The expression has now been simplified to: 3x³ + 7x + x/3. If x = 3, then the solution is (3(3³) + 7(3) + x/3) = (3(27) + 21 + 1) = 103.
A variable expression can be part of an equation, if there is an equals sign between it and another expression, or value. First, simplify each side of the equation and then solve it. For example in the equation: x + 7(3x) = 22, first multiply (7 x 3x) and then add (x + 21x = 22x). If 22x = 22, then multiply both sides of the equation by (1/22) to get the value for x: (1/22)22x = (1/22)22, resulting in a solution of x = 1. This can be checked by substitution in the original equation.