Expanding Single Brackets

Basic Concept

• To expand brackets, multiply each term inside the bracket by the term outside.
• Example:
  • If given 4(x + 2), multiply:
    • 4 * x results in 4x
    • 4 * 2 results in 8
  • Final expanded form: 4x + 8

Examples

• Example 1: 9(x - 9)

  • Perform multiplication:
    • 9 * x results in 9x
    • 9 * -9 results in -81
  • Expanded form: 9x - 81

• Example 2: Positive terms outside

  • For 4(x + 2):
    • Direct multiplication gives 4x + 8
  • For 9(x - 9):
    • Multiplication gives 9x - 81

Special Cases

• When a letter is outside:

  • Example: x(x + 3)
    • x * x results in x^2
    • x * 3 results in 3x
  • Expanded form: x^2 + 3x

• Negative numbers outside brackets:

  • Example 3: -5(2x + 3)

    • -5 * 2x yields -10x
    • -5 * 3 yields -15

  • Expanded form: -10x - 15

  • Example 4: -3(2x - 5)

    • -3 * 2x yields -6x
    • Negative times negative: -3 * -5 results in +15

  • Expanded form: -6x + 15

Key Points

• Always multiply each term inside the bracket by the term outside.
• Be careful with signs, especially when dealing with negatives.
• Negative times negative yields a positive outcome.