In Algebra, Math expressions are the combination of variables, operators (signs) and constants.

Example: $a + 7$

In any math expression, a variable can change its value any time, but in case of constants the value remains the same.

## What are Math Expressions?

An algebraic expression is a number, a variable or a combination of the two factors connected by mathematical operations like addition, subtraction, multiplication, and division.

For example : $4x, 3p, 2a+b,$$\frac{6z}{5}$

## What is an expression in Math?

An expression in math would be considered as a statement that will use numbers, variables or in some cases both. In order to write a math expression given out in a math problem one has to interpret the text very well.

### Examples of Math Expressions

Given below are some examples of mathematical expressions:

• $x$
• $3x$
• $7 + 3x$
• If one person is older than the other by 6 years, then the math expression for the person would be $6 + p$

## Math Expressions and Equations

A math expression is a collection of one or more terms, which are separated by the signs ( + , - , x , / ).

Example : $8 + b$ or $a - 3$

In algebra, an equation is a mathematical statement with two expressions where, each expression is separated by an equal (=) sign. Variables can be present on both the sides of the equality (=) sign and we use letters to denote such variables.

Example 1: $x = 4 + 2$ , [Here, we can observe that the variable is present only on one side of the equation].

Example 2: $2x + 3 = x + 4$ , [Here, we can observe that the variables are present on both side of the equation].

## Simplifying Math Expressions

We usually simplify math expressions to get a normal result. If the expression contains a parenthesis, we often use the distributive property rule to remove these parenthesis and for combining similar terms.

### Examples on Simplifying Math Expressions

Some examples on simplifying math expressions.

Example 1:

Simplify expression $3x + 6 + 4x - 2$

Solution:

Given $3x + 6 + 4x - 2$

$3x + 6 + 4x - 2$ = $3x + 4x + 6 - 2$ (Commutative property)
= $(3x + 4x) + (6 - 2)$ (Associative property)
= $(3 + 4) x + (6 - 2)$ (Distributive property)
= $7x + 4$ (Combining like terms)

Answer: $7x + 4$

Example 2:

Simplify the expression $2(x - 4) + (3 - 5x)$

Solution:

Given $2(x - 4) + (3 - 5x)$

$2(x - 4) + (3 - 5x)$ = $2x - 8 + 3 - 5x$ (Distributive property)
= $2x - 5x - 8 + 3$ (Combining like terms)
= $- 3x - 5$

Answer: $- 3x - 5$

Example 3:

Simplify the expression $5x - 8 + x - 1$

Solution:

$5x - 8 + x - 1$ = $5x + x - 8 - 1$ (Combining like terms)
= $6x - 9$

Answer: $6x - 9$

Example 4:

Simplify the expression $3(x - 2) + 6$

Solution:

$3(x - 2) + 6$ = $3x - 6 + 6$ (Distributive property)
= $3x$ (Combining like terms)

Answer: $3x$

## Solving Math Expressions

Given below are steps to solve math expressions
• Group the terms carrying the same variable in the given math expression.
• Do the mathematical operations in the brackets for simplifying the variable.
• Do the multiplication and division operations starting form left to right.
• Do the addition and subtraction operations from left to right.

### Examples on Solving Math Expressions

Given below are some examples on solving math expressions.

Example 1:

Simplify $4x^{2} + 7 + x^{2} + 5 + x$

Solution:

Group the terms carrying the same variable
$4x^{2} + 7 + x^{2} + 5 + x = (4x^{2} + x^{2}) + x + (7 + 5)$
$= (5x^{2}) + x + (12)$
$= 5x^{2} + x + 12$

$5x^{2} + x + 12$

Example 2:

Simplify $3(4x^{2} + 7x - 2) + 4(6x + 2) - 6x^{2}$

Solution:

Rewrite the expression by using the Distributive Property.
$3(4x^{2} + 7x - 2) + 4(6x + 2) - 6x^{2} = 3(4x^{2}) + 3(7x) - 3(2) + 4(6x) + 4(2) - 6x^{2}$
$= 12x^{2} + 21x - 6 + 24x + 8 - 6x^{2}$
$= (12x^{2} - 6x^{2}) + (21x + 24x) + (8 - 6)$
$= 6x^{2} + 45x + 2$

$6x^{2} + 45x + 2$

## Examples on Math Expressions

Given below are some examples on solving math expressions.

Example 1:

Simplify $5x^{2} + 17 + 3x^{2} + 3 + 2x$

Solution:

Group the terms carrying the same variable
$5x^{2} + 17 + 3x^{2} + 3 + 2x = (5x^{2} + 3x^{2}) + 2x + (17 + 3)$
$= (8x^{2}) + 2x + (20)$
$= 8x^{2} + 2x + 20$

$8x^{2} + 2x + 20$

Example 2:

Simplify $3(4x^{2} + 7x - 2) + 4(6x + 2) - 6x^{2}$

Solution:

Rewrite the expression by using the Distributive Property.
$4(3x^{2} + 2x - 7) + 6(2x + 4) - 5x^{2} = 4(3x^{2}) + 4(2x) - 4(7) + 6(2x) + 6(4) - 5x^{2}$
$= 12x^{2} + 8x - 28 + 12x + 24 - 5x^{2}$
$= (12x^{2} - 5x^{2}) + (8x + 12x) + (24 - 28)$
$= 7x^{2} + 20x - 4$

$7x^{2} + 20x - 4$

Example 3:

Simplify expression $6x + 3 + 2x - 4$

Solution:

Given $6x + 3 + 2x - 4$

$6x + 3 + 2x - 4$ = $6x + 2x + 3 - 4$ (Commutative property)
= $(6x + 2x) + (3 - 4)$ (Associative property)
= $(6 + 2)x + (3 - 4)$ (Distributive property)
= $8x - 1$ (Combining like terms)

Answer: $8x - 1$

Example 4:

Simplify the expression $4(x - 3) + (4 - 2x)$

Solution:

Given $4(x - 3) + (4 - 2x)$

$4(x - 3) + (4 - 2x)$ = $4x - 12 + 4 - 2x$ (Distributive property)
= $4x - 2x - 12 + 4$ (Combining like terms)
= $2x - 8$

Answer: $2x - 8$

Example 5:

Simplify the expression $15x - 3 + 5x - 12$

Solution:

$15x - 3 + 5x - 12$ = $15x + 5x - 3 - 12$ (Combining like terms)
= $20x - 15$

Answer: $20x - 15$

Example 6:

Simplify the expression $4(x - 1) + 3$

Solution:

$4(x - 1) + 3$ = $4x - 4 + 3$ (Distributive property)
= $4x - 1$ (Combining like terms)

Answer: $4x - 1$

## Math Expressions Practice Problems

Given below are some of the practice problems on math expressions.

1. Simplify $12x^{2} + 11 + 23x^{2} + 31 + 12x$
2. Simplify $13(4x^{2} + 3x - 3) + 3(5x + 6) - 3x^{2}$
3. Simplify expression $16x + 7 + 3x - 9$
4. Simplify the expression $8(x - 7) + (7 - x)$
5. Simplify the expression $9x - 6 + 3x - 12$
6. Simplify the expression $7(x - 12) + 32$