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View submission: Ask Anything Wednesday - Engineering, Mathematics, Computer Science
(a-1)(a+2)
= a^2 + 2a - a - 2
= a^2 + a - 2
= a(a+1) - 2
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Generalization 1:
(a-1)(a+n)
= a^2 + n.a - a - n
= a^2 + (n-1)a - n
= a (a+(n-1)) - n
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Generalization 2:
(a-m)(a+n)
= a^2 + n.a -m.a -m.n
= a^2 +(n-m)a - m.n
= a (a+(n-m)) -m.n
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So, you see, in the end it's just algebra, really.
There's nothing here!