Work Step by Step
$(a-b)^3=(a-b)(a-b)(a-b)=(a^2-ab-ab+b^2)(a-b)=(a^2-2ab+b^2)(a-b)=a^3-2a^2b+b^2a-a^2b+2ab^2-b^3=a^3-3a^2b+3ab^2-b^3$ Thus we proved what we had to.
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