Math CentralQuandaries & Queries


Question from Jacky, a parent:


Hi Jacky,

To a large extent factoring involves recognizing patterns. In the expression

x2 - y2 + 4x + 4y

The pattern I recognize is x2 - y2 which can be factored as a difference of squares

x2 - y2 = (x - y)(x + y)

Can you now see how to complete the problem?

If you need further assistance write back,

Jacky wrote back

Back to Penny's reply. Of course, I know the expression but I would like to
seek for the simplest expression other than:

(X+Y)(X-Y+4) ?


I don't think there is a simpler form unless it's the original x2 - y2 + 4x + 4y. The simplest or most useful form of a mathematical expression depends on how you are going to use the expression. Writing an expression in factored form as you did here, (x + y)(x - y + 4), is quite often the most usual way to express it.


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