FACTORISATION USING CROSS-METHOD

Cross-method.

 Sometimes a quadratic expression can have more than 2 terms in it. Thus, we would have to use another method to factorise it. To be able to apply this method into the expression, the expression must first have 3 terms and must be a quadratic expression.
Some examples to illustrate this would be:
 c2-4cd-21d2
To do this, we need a table to put in all our terms. Remember that the terms have to be put in this order:

 First term in the first column
 Last term in the second column
 Middle term in the final column

àDraw the way that is done in the picture. àPut in the terms following the position that is given. àThe terms written before the line will have their numbers    multiplying together from top to bottom. àThe term that is written after the vertical line would have       the answers adding together to get the answer.     è After finding out what values are needed to be multiplied to get the answers, cross multiply the answers and write them after the vertical line.   è Add them together and ensure that the answer is what is written.

In the context of the question given, we would have to do and ensure that the answer is the same as the terms written underneath the horizontal line. Do remember to take extra notice of the signs of the terms.Thus, the factorized form for c²-4cd-21d² is (c+3d)(c-7d). 



Let's take a look at another example using the cross-method.

2x²-7xy+6y²

Doing exactly the same thing like we did earlier, we would come to an answer of (x-2y)(2x-3y).