Question : What is the value of $(a-b)^3 - a^3 + b^3$?
Option 1: $3ab(a-b)$
Option 2: $-3ab(a+b)$
Option 3: $3ab(a+b)$
Option 4: $-3ab(a-b)$
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Correct Answer: $-3ab(a-b)$
Solution : $(a-b)^3 - a^3 + b^3 $ Using the algebraic identity, $(a-b)^3 = a^3 - b^3 - 3ab(a-b)$ ⇒ $(a-b)^3 - a^3 + b^3$ = $a^3 - b^3 - 3ab(a-b) - a^3 + b^3$ = $- 3ab(a-b)$ Hence, the correct answer is $-3ab(a-b)$.
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