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(a+b)^2 = (a^2+2ab+b^2) (a-b)^2 = (a^2-2ab+b^2) (a+b)(a-b) = (a^2+b^2)

a^n+a^n = a^n+n ((a^n)/(a^n)) = a^n-n (a^n)^n = a^n x n (ax)^n = (a^n) (x^n)

a^-n = 1/(a^n)

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