MNM for Students
  • Home
  • Find a Topic
    • Number: Properties and calculations >
      • Calculations with whole numbers >
        • Written multiplication methods
        • Multiply using the grid method
        • Multiply using Napier's Rods
        • Long multiplication
        • Simple short division
      • Rounding and estimation >
        • Rounding to the nearest whole number
        • Rounding to decimal places
      • Factors, multiples and primes >
        • What is a factor?
        • What is a multiple?
        • What is a prime number?
        • Product of prime factors
      • Powers (indices) >
        • Square numbers
        • Cube numbers
        • What is a power?
        • Simple power laws
    • Number: Fractions, decimals and percentages >
      • Fractions >
        • Equivalent fractions
        • Improper fractions to mixed numbers
        • Mixed numbers to improper fractions
        • Finding halves and quarters
        • Finding fractions of amounts
        • Comparing fractions
        • Writing as a fraction
        • Adding and subtracting simple fractions
      • Decimals >
        • Multiplying a decimal by an integer
        • Multiplying two decimals mentally
        • Multiplying two decimals (written)
      • Percentages >
        • What is a percentage?
        • Easy percentages
        • Percentages without a calculator
        • Percentages with a calculator
    • Algebra: Basic skills >
      • Introduction to algebra >
        • Algebraic notation
        • Writing expressions using algebra
        • Order of operations in algebra
      • Expand, factorise and simplify >
        • Expanding single brackets
      • Formulae and substitution >
        • What is a formula?
        • Simple substitution
        • Substituting into formulae
      • Quadratic expressions >
        • What does quadratic mean?
        • Expanding simple quadratics
        • Factorising simple quadratics
    • Algebra: Graphs >
      • Linear (straight line) graphs >
        • Finding the gradient from two points
        • Finding the gradient from a graph (linear)
        • Midpoint of a line segment
    • Algebra: Equations and inequalities >
      • Inequalities >
        • Inequality symbols
        • Simple inequalities using algebra
        • Inequalities on a number line
        • Solving two-step inequalities
    • Shape: Calculations and measures >
      • Area of 2D shapes >
        • Area of a triangle
        • Area of a parallelogram
      • Circles >
        • Parts of a circle
        • Circumference of a circle
        • Area of a circle
      • Pythagoras' theorem
      • Trigonometry in right angled triangles >
        • Introduction to trigonometry
        • Finding a missing angle (SOHCAHTOA)
    • Shape: Properties and constructions >
      • Angles >
        • Naming and classifying angles
        • Angles in a triangle
        • Angles in a quadrilateral
      • 3D shapes
      • Polygons >
        • What is a polygon?
        • Naming polygons
        • Angle sum in a polygon
        • Regular polygons
        • Interior angles in regular polygons
        • Exterior angles
      • Constructions >
        • Bisecting an angle
    • Probability >
      • Experimental and theoretical >
        • Relative frequency (experimental probability)
        • Using probability to estimate outcomes
  • Mastery Pathway
    • Elementary 1
    • Elementary 2
    • Elementary 3
    • Elementary 4
    • Intermediate 1
    • Intermediate 2
  • GCSE Exam Preparation
    • IGCSE Foundation >
      • Revision guide
    • GCSE Higher (to 2015) >
      • November 2012 Paper 1 (Solutions)
  • Links
  • 10H

Expanding simple quadratics


When we expand an expression in algebra, we multiply out the brackets. The picture above shows the link between expanding quadratic brackets (sometimes called "double brackets") and areas. 
Picture
The important thing when expanding quadratic expressions is to remember to multiply everything in the first bracket by everything in the second bracket. There are some little "tricks" that you can use to help you to do this.

You can use the grid method, based on the method used for normal multiplication.

You can use FOIL to remind you to multiply all of the terms. FOIL tells you to:
  1. Multiply the FIRST terms
  2. Multiply the OUTSIDE terms
  3. Multiply the INSIDE terms
  4. Multiply the LAST terms.


Or you can use the "smiley face" method - it's just called this because it makes something that looks vaguely like a smiley face. This is really just a more visual version of FOIL, and it just reminds you to multiply all of the terms together.

You must also remember to simplify your answer at the end by collecting like terms. Remember that we can't put x² terms with x terms because they represent different things. Normally, you will have to simplify two x terms.
Picture

Picture

First Steps

Picture

More Like This

Next Steps

Next Steps


External links


Privacy Policy