Mathematical expression is a series of numbers which are joined together with different mathematical operators. In order to solve the series of these numbers, we need to know a particular order which is to be followed to get the solution to the mathematical expressions. Else, every time the mathematical expression is solved, you will get a different result. |

Expression contain variables and are generally represented by english alphabets like p, q, x, y, a, b etc. The expressions can be of several types and have different descriptions for different representations of the relationships of the variables and the constants. Variable represents any unknown quantity that holds certain numeric value and has to be evaluated in most of the mathematical expressions.

In different expressions, we may use the same name of the variable. But, the values can differ from one expression to another.

**Mathematical expression**represents a numeric value and an expression does not contain an 'equal to' (=) sign. It is a string of mathematical symbols placed on one side of an equation and an expression will have no solution. Two most common types of mathematical equation is arithmetic and algebraic equation.

Examples of mathematical expressions are 5 + 5, (88 - 15) + 8, $\sqrt{569}$ + 2, 3xy + 7y etc.,

**Mathematical equation**is a mathematical sentence that says two things are equal. It can be solved and indicates the equality of two expressions, sequence of symbols is split into left and right sides joined by an equal sign.

Examples of mathematical equations are 3x + 5y = 12, x + y + z = 10, $\frac{7}{5}$x + $\frac{1}{3}$ z = 5

Given below are some of the examples of mathematical expressions.

### Solved Examples

**Question 1:**Solve 3x$^{2}$ + 2x + 4 = 0.

**Solution:**

__Step - 1:__Coefficients of a, b and c are 3, 2 and 4 respectively.

The quadratic equation formula is

x = $\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$

__Step - 2:__Plug in the values of a, b and c in the above formula.

x = $\frac{-2\pm\sqrt{2^{2}-4 \times 3 \times 4}}{2 \times 3}$

__Step - 3:__Simplify the expression under the square root.

x = $\frac{-2\pm\sqrt{-44}}{6}$

Solving for x, we get

$x_{1}$ = $\frac{-2+\sqrt{-44}}{6}$

$x_{1}$ = -$\frac{1}{3}$ + $\frac{1}{3}$ $\sqrt{11i}$

$x_{2}$ = $\frac{-2-\sqrt{-44}}{6}$

$x_{2}$ = -$\frac{1}{3}$ - $\frac{1}{3}$ $\sqrt{11i}$

__Step - 4:__Therefore, the solutions for the given equation are as follows:

$x_{1}$ = -$\frac{1}{3}$ + $\frac{1}{3}$ $\sqrt{11i}$ and $x_{2}$ = -$\frac{1}{3}$ - $\frac{1}{3}$ $\sqrt{11i}$

**Question 2:**Evaluate 2x$^{4}$ + 3x$^{3}$ - 5x$^{2}$ + 7y for x = -2, y = 1.

**Solution:**

**Given:**2x$^{4}$ + 3x$^{3}$ - 5x$^{2}$ + 7y

In the given expression, plug in x = -2 and y = 1

= 2(- 2)$^{4}$ + 3(- 2)$^{3}$ - 5(- 2)$^{2}$ + 7(1)

= 2 x 16 - 24 - 20 + 7

= 39 - 44

= -5