Variable Expressions
2026-02-28 11:30 Diff
https://brightchamps.com/en-us/math/algebra/variable-expressions

Operations on expressions involve applying mathematical procedures such as addition, subtraction, multiplication, division, and factoring to expressions involving one or more variables. The main types of operations are: 
 

  • Adding and subtracting expressions
     
  • Multiplication of expressions
     
  • Division of expressions
     
  • Solving expressions
     
  • Factoring expressions
     
  • Expanding expressions

Adding and subtracting expressions: Addition and subtraction are the basic arithmetic operations. In addition, we combine the like terms in the expressions. 

For example, \((3x + 5) + (5x + 4) = (3x + 5x) + (5 + 4) = 8x + 9\)

In subtracting expressions, the like terms from the second expression are subtracted from the corresponding like terms from the first expression. 

For example, \((6x+ 3) - (2x + 1) = (6x - 2x) + (3 - 1) = 4x + 2\)

Multiplication of expressions: To multiply expressions, we use the distributive property of multiplication, that is, \(a(b + c) = ab + ac\). 

For example, multiplying \(3x + 4\) with 5x

Using the distributive property of multiplication: \(a(b + c) = ab + ac\)

\(5x(3x + 4) = (5x × 3x) + (5x × 4)\\[1em] 5x(3x + 4)= 15x^2 + 20x\)

Division of expressions: The division of expressions is used to simplify the expressions. Here, the expressions are divided by separate terms, by factoring or simplifying common terms. 

For example, \(24x^2 + 36x\) by \(6x\)

\((\frac{24x^2}{6x}) + (\frac{36x}{6x}) = 4x + 6\)


Solving expressions: Solving expressions involves substituting the variables with the given value to find the result. For example, solve \(5x^2 + 5x\) for \(x = 2\) and \(x = 5\)

If \(x = 2\):

\(5x^2 + 5x = 5(2)^2 + 5(2) = 5(4) + 10 = 20 + 10 = 30\)

If \(x = 5\): 

\(5x^2 + 5x = 5(5)^2 + 5(5) = 5(25) + 25 = 125 + 25 = 150\)


Factoring expressions: Factoring expressions is the way of expressing an expression as the product of its factors. In this method, we first factor out the greatest common factor of the expression. 

For example, factoring \(36x + 54\)

The GCF of 36 and 54 is 18

So, \(36x + 54 = 18(2x + 3)\)

Expanding expressions: Expanding expressions is the opposite of factoring, as here we remove the parentheses by multiplying the value out of the expression with the expression inside the parentheses. 

For example, expanding the expression 18(2x + 3)

\(18(2x + 3) = (18 × 2x) + (18 × 3)\\[1em] 18(2x + 3)= 36x + 54\)