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January 16th, 2017, 09:17 PM   #1
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Maths Formula

how you can show (a+b)^2 = a^2 + 2ab + b^2
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January 16th, 2017, 09:38 PM   #2
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Quote:
Originally Posted by Logicalbaniya View Post
how you can show (a+b)^2 = a^2 + 2ab + b^2
It's the standard multiplication of the two binomials $(a + b)(a + b)$. There's an acronym for this, FOIL: First, Outside, Inside, Last. So

$(a + b)(a + b)$

$= a^2 + ba + ab + b^2 = a^2 + 2ab + b^2$

In other words: First, $a \times a$. Outside, $a \times b$. Inside, $b \times a$. Last: $b \times b$. Then collect terms.

Another way to interpret this question is to write out a formal proof from axioms, carefully noting each use of the distributive law, commutative laws, associative laws, etc.

Which interpretation are you asking? How to do it, or how to prove it from axioms?

Last edited by Maschke; January 16th, 2017 at 09:44 PM.
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