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how is (a+b)^2 = a^ + b^2 + 2ab?
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It is just a rule that you need to know. To explain it, you can imagine that (a + b)^2 is equal to (a + b) x (a + b). If we were to multiply everything out, we would get a^2 + ab + ba + b^2 and that would give us a^2 + 2ab + b^2.
