HL
11 tháng 1 2023 lúc 21:14
\(\left[x^3-3xy\left(x-y\right)-y^3\right]-x^2+2xy-y^2\)
\(=\left(x^3-y^3\right)-3xy\left(x-y\right)-\left(x^2-2xy+y^2\right)\)
\(=\left(x-y\right)\left(x^2+xy+y^2\right)-3xy\left(x-y\right)-\left(x-y\right)^2\)
\(=\left(x-y\right)\left(x^2+xy+y^2-3xy-x+y\right)\)
\(=\left(x-y\right)\left(x^2-2xy+y^2-x+y\right)\)
\(=\left(x-y\right)\left[\left(x-y\right)^2-\left(x-y\right)\right]\)
\(=\left(x-y\right)\left(x-y\right)\left(x-y-1\right)\)
\(=\left(x-y\right)^2\left(x-y-1\right)\)
\(=8^2\left(8-1\right)\\ =64\cdot7=448\)
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