07Cfactorising4terms

toc = Factorising Four Terms =

Grouping Terms 2 and 2
If the expression has four terms and there are no common factors, it can sometimes be factorised by grouping the terms into pairs and factorising each pair separately.

You may need to rearrange the terms so that pairs with a common factor are together. {don't forget: any minus sign belongs with the term that comes after it}

** Example 1 **
math \textbf{(a)} \quad \text{Factorise : } xy + 5x + 5y + 25 math



math \textbf{(b)} \quad \text{Factorise : } ax - 3y + 3x - ay math



Grouping then Difference of Two Squares
Sometimes, after grouping in pairs, we will get a Difference of Two Squares

** Example 2 **
math \text{Factorise : } x^2 - y^2 + 3x - 3y math



Grouping Terms 3 and 1
Sometimes grouping terms 2 and 2 does not work, see example 3a:

** Example 3a **
math \text{Factorise : } x^2 + 10x + 25 - 4y^2 math

When this happens, try grouping 3 of the terms together. This might produce a difference of two squares.

** Example 3b **
math \text{Factorise : } x^2 + 10x + 25 - 4y^2 math




 * NOTE **: Many expressions of 4 terms cannot be fully factorised.

.