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Algebraic identities are equations where the value of the left-hand side of the equation is identically equal to the value of the right-hand side of the equation. The expression (x-y)3 is a cubic expression.
Answer: The expansion of (x-y)3 is x3 - y3 - 3x2y + 3xy2
Let us see how to expand (x-y)3.
The expression (x-y)3 can be written as, (x-y)(x-y)(x-y)
First simplify (x-y)(x-y) by binomial multiplication.
(x-y)(x-y) = x2 - 2xy + y2
Now multiply (x-y) with x2 - 2xy + y2
(x-y)(x-y)(x-y) = (x-y)(x2 - 2xy + y2)
= x3 - 2x2y + xy2 - yx2 + 2xy2 - y3
= x3 - 3x2y + 3xy2 - y3
Thus, the expansion of (x-y)3 is x3 - y3 - 3x2y + 3xy2