\(A=\left(x^3-y^3\right)-6xy\)
\(A=\left(x-y\right)\left(x^2+xy+y^2\right)-6xy\)
\(A=2x^2+2xy+2y^2-6xy\)
\(A=2x^2-4xy+2y^2=2\left(x-y\right)^2\)
\(A=2.2^2=2.4=8\)
Vì \(x-y=2\)
\(\Leftrightarrow x=2+y\)(1)
Thế (1) vào \(A\)ta có :
\(A=\left(2+y\right)^3-6\left(2+y\right)y-y^3\)
\(A=8+12y+6y^2+y^3-12y-6y^2-y^3\)
\(A=8\)
Đáp án : 8
\(A=x^3-6xy-y^3\)
\(\Rightarrow A=\left(x^3-y^3\right)-6xy\)
\(\Rightarrow A=\left(x-y\right)\left(x^2+xy+y^2\right)-6xy\)
\(\Rightarrow A=2.\left(x^2+xy+y^2\right)-6xy\)
\(\Rightarrow A=2.\left(x^2+xy+y^2-3xy\right)\)
\(\Rightarrow A=2.\left(x^2-2xy+y^2\right)\)
\(\Rightarrow A=2.\left(x-y\right)^2\)
\(\Rightarrow A=2.2^2\)
\(\Rightarrow A=2^3\)
\(\Rightarrow A=8\)
