An introduction to completing the square. What it means, why we do it and how a visual explanation of how it works.
This is the first in a series of videos on completing the square. Other videos will be available soon looking at:
- Writing quadratic expressions in completed square form
- Using completing the square to solve quadratic equations
- Using completing the square to draw graphs of quadratic functions
How to use the quadratic formula to solve quadratic equations. Including leaving answers in surd form.
How to solve quadratic equations by factorising into double brackets. Including equations where the coefficient (number in front) of the squared term is more than 1.
How to factorise a quadratic expression into two brackets (binomials) including when the coefficient (number in front) of the squared term is more than 1.
An example of factorising an expression into a single bracket.
A simple example of expanding (multiplying out) double brackets
(x + 3)(x – 4)
For more on this topic, see expanding-double-brackets
Expanding (multiplying out) double brackets using the FOIL method to ensure that all the terms are multiplied.
The expressions in the brackets are called binomials because they consist of two terms that are either added or subtracted.
After multiplying the binomials it is important to simplify the final expression by collecting like terms.