Question

# If AB + BA = 0, then prove that A3 --B3 = (A + B) (AP - AB-B4). D2

Solution a3 – b3 = (a - b)(a2 + ab + b2)
you know that
(a - b)3 = a3 + 3ab(a - b) – b3
then a3 – b3 = (a - b)3 + 3ab(a - b)
= (a - b)[(a - b)2 + 3ab]
= (a - b)(a2 – 2ab + b2 + 3ab)
= (a - b)(a2 + ab + b2 )

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