Question

cho x-y=11. tính giá trị của biểu thức

M=x³-3xy(x-y)-y³-x²+2xy-y²

Answer 1

\(M=x^3-3xy\left(x-y\right)-y^3-x^2+2xy-y^2\)

\(=x^3-3x^2y+3xy^2-y^3-\left(x^2-2xy+y^2\right)\)

\(=\left(x-y\right)^3-\left(x-y\right)^2\)

Có: x - y = 11 \(\Rightarrow\left(x-y\right)^3-\left(x-y\right)^2=11^3-11^2=1210\)

Vậy M = 1210

Answer 2

\(M=x^3-3xy\left(x-y\right)-y^3-x^2+2xy-y^2\)

\(=\left[x^3-3xy\left(x-y\right)-y^3\right]-\left[x^2-2xy+y^2\right]\)

\(=\left(x-y\right)^3-\left(x-y\right)^2\)

Thay \(x-y=11\) vào \(\left(x-y\right)^3-\left(x-y\right)^2\) , ta được :

\(\left(x-y\right)^3-\left(x-y\right)^2\)\(=11^3-11^2=1210\)