Simplifying

Simplifying Algebraic Expressions

Understanding Variables and Constants

  • In algebra, variables are symbols (typically letters) that represent unknown numbers or values.
  • Constants are numbers with a fixed value.

Understanding Algebraic Expression

  • An algebraic expression is made up of variables, constants, and mathematical operations.
  • An example of an algebraic expression is 5x + 2y – 3.

Constants within Algebraic Expressions

  • Constants within an algebraic expression can sometimes be combine, this is known as simplifying constants.
  • For example , in 5 + 3x - 2 , the constant 5 and -2 can be added together to simplify the expression to 3x + 3.

Like and Unlike Terms

  • Like terms are terms that contain the same variables with the same powers.
  • Unlike terms are terms that contain different variables, or the same variables with different powers.
  • For instance, in 3x + 5x, 3x and 5x are like terms because they all have ‘x’ as their variable. In contrast, in the expression 4x + 2y, 4x and 2y are unlike terms.

Combining Like Terms

  • Like terms can be combined together to simplify the algebraic expression.
  • For example, in the expression 5x + 3x, the like terms 5x and 3x can be combined together to form 8x, therefore simplifying the expression.

Removing Brackets

  • Sometimes, algebraic expressions contain brackets, which indicate that the operations within the brackets should be completed before the operations outside the brackets.
  • To simplify expressions with brackets, apply the distributive law. This means multiplying the term outside the bracket by each term inside the bracket.
  • For instance, for the expression 4(2x + 3), multiply 4 by both 2x and 3 to get 8x + 12.

Order of Operations

  • When simplifying complex algebraic expressions, follow the order of operations which is often remembered as BIDMAS/BODMAS: Brackets/Orders (powers and roots), Division and Multiplication (left-to-right), Addition and Subtraction (left-to-right).

Factorisation

  • Factorisation is the process of breaking down an algebraic expression into its simplest form.
  • For instance, x² + 2x can be factorised into x(x + 2).