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Question
Factorize each of the following expressions:
x3 − 2x2y + 3xy2 − 6y3
Solution
\[x^3 - 2x^2 {y + 3xy}^2 - 6y^3 \]
\[ = ( x^3 - 2 x^2 y) + (3x y^2 - 6 y^3 )\] [Grouping the expressions]
\[ = x^2 (x - 2y) + 3 y^2 (x - 2y)\]
\[ = ( x^2 + 3 y^2 )(x - 2y)\] [Taking (x - 2y) as the common factor]
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