Difference Of Two Squares & Cross Method
In this video, we will start by learning how to expand expressions using the perfect square identity, which helps simplify squares of binomials. Next, we will explore the Difference of Two Squares identity, learning how to expand and factorise expressions of the form \((a^2 – b^2) =(a+b)(a-b)\). Finally, we will cover factorisation using the cross method, a step-by-step technique useful for factorising quadratic expressions efficiently.
This course is an extension of the factorisation course by Common Factor and Grouping.
Related Lessons:
Perfect Square Identity
The Perfect Square Identity is mainly useful for expansion and has limited use in factorisation, as it can be challenging to recognize whether an expression fits the pattern. For students who find it difficult to apply the Perfect Square Identity, a reliable alternative is to use the rainbow expansion method for normal expansion.
\(\left(a+b\right)^2=a^2+2ab+b^2\)
\(\left(a-b\right)^2=a^2-2ab+b^2\)
Difference Of Two Squares Expansion
In this video course, we will learn the patterns for applying the Difference of Two Squares identity in expansion. We will focus on how to recognise when the identity can be used and how to apply it efficiently and accurately.
Difference Of Two Squares Factorisation
In this video course, we will learn how to factorise expressions using the Difference of Two Squares identity. Students will discover how to identify suitable patterns and apply the identity accurately to break expressions into their simplest factors.
Cross Method Factorisation
The cross method is a step-by-step technique used to factorise quadratic expressions efficiently. It helps find two factors that can multiply together to get the original expression. The quadratic expression must be in the form \(ax^2+bx+c\).
Note that not all quadratic expressions can be factorised using the cross method. In a future course, we will learn how to use the quadratic formula to determine the factors of any quadratic expression.