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(a + b)2 = a2 + 2ab + b2
(a − b)2 = a2 − 2ab + b2
a2 + b2 = (a + b)2 − 2ab
a2 + b2 = (a − b)2 + 2ab
(a + b)3 = a3 + b3 + 3ab(a + b)
(a − b)3 = a3 − b3 − 3ab(a − b)
a3 + b3 = (a + b)3 − 3ab(a + b)
a3 − b3 = (a − b)3 + 3ab(a − b)
a2 − b2 = (a + b)(a − b)
a3 − b3 = (a − b)(a2 + ab + b2)
a3 + b3= (a + b)(a2 − ab + b2)
a4 – b4 = (a2 – b2)(a2 + b2) = (a + b)(a + b)(a2 + b2)
a4 + b4 = (a2 + b2)2 – 2a2b2 = (a2 + √2ab + b2)(a2 – √2ab + b2)
a5 + b5 = (a + b)(a4 – a3b + a2b2 – ab3 + b4 )
a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)
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