\(A=x\left(x+2\right)+y\left(y-2\right)-2xy\)
\(\Leftrightarrow A=x^2+2x+y^2-2y-2xy\)
\(\Leftrightarrow A=\left(x-y\right)^2+2\left(x-y\right)\)
\(\Leftrightarrow A=10^2-2.10\)
\(\Leftrightarrow A=80\)
\(A=x\left(x+2\right)+y\left(y-2\right)-2xy\)
\(=x^2+2x+y^2-2y-2xy\)
\(=\left(x^2-2xy+y^2\right)+\left(2x-2y\right)\)
\(=\left(x-y\right)^2+2\left(x-y\right)\)
\(=10^2+2.10=120\)
\(A=x^2+2x+y^2-2y-2xy=\left(x^2-2xy+y^2\right)+\left(2x-2y\right)=\left(x-y\right)^2+2\left(x-y\right)=\left(x-y\right)\left(x-y+2\right)\)
\(=10\left(10+2\right)=10.12=120\)
Bạn ghi thiếu đề. Đáng lẽ đề phải như này:
\(A=x\left(x+2\right)+y\left(y-2\right)-2xy+37\)
\(=x^2+2x+y^2-2y-2xy+37\)
\(=\left(x^2+y^2-2xy\right)+\left(2x-2y\right)+37\)
\(=\left(x-y\right)^2+2\left(x-y\right)+37\)
Thay \(x-y=7\) vào biểu thức, ta có:
\(A=7^2+2.7+37\)
\(=49+14+37\)
\(=100\)
\(x\left(x+2\right)+y\left(y-2\right)-2xy\)
\(=x^2+2x+y^2-2y-2xy\)
\(=\left(x^2-2xy+y^2\right)+\left(2x-2y\right)\)
\(=\left(x-y\right)^2+2\left(x-y\right)\)
\(\left(x-y\right)\left(x-y+2\right)\)
