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Go Backwards

Man running backwards on track

Try to solve the problem backwards! It can often be easier to approach the problem from the end, rather than from the beginning.

This approach won’t always work, but it works very well in those cases where you already know the answer. For example, if the exercise begins with “Show that \ldots".

Look at the exercise “Show that a2+2ab+b2a^2+2ab+b^2 can be written as (a+b)2(a+b)^2”. The backwards approach here is to try to write (a+b)2(a+b)^2 as a2+2ab+b2a^2+2ab+b^2:

(a+b)2=(a+ b)(a+b)=aa +ba +ab+ bb=a2+2ab+b2\begin{aligned} (a + b)^2 &= (a + b)(a + b) \\ &= aa + ba + ab + bb \\ &= a^2 + 2ab + b^2 \end{aligned}
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