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

\(\Leftrightarrow A=x^2+2x+y^2-2y-2xy\)

\(\Leftrightarrow A=\left(x-y\right)^2+2\left(x-y\right)\)

\(\Leftrightarrow A=10^2-2.10\)

\(\Leftrightarrow A=80\)

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

\(=x^2+2x+y^2-2y-2xy\)

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

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

\(=10^2+2.10=120\)

1, \(x^2+4x-2xy-4y+y^2=\left(x^2-2xy+y^2\right)+\left(4x-4y\right)=\left(x-y\right)^2+4\left(x-y\right)=\left(x-y\right)\left(x-y+4\right)\)

2, \(x^3-2x^2+x=x\left(x^2-2x+1\right)=x\left(x-1\right)^2\)

3, \(2x^2+4x+2-2y^2=2\left(x^2-y^2\right)+2\left(2x+1\right)=2\left(x^2+2x+1-y^2\right)=2\left[\left(x+1\right)^2-y^2\right]=2\left(x+1-y\right)\left(x+1+y\right)\)

4, \(x^4-2x^2=x^4-2x^2+1-1=\left(x^2-1\right)^2-1=\left(x^2-1-1\right)\left(x^2-1+1\right)=\left(x^2-2\right)x^2\)

5, \(x^3+2x^2y+xy^2-9x=x\left(x^2+2xy+y^2-9\right)=x\left[\left(x+y\right)^2-3^2\right]=x\left(x+y-3\right)\left(x+y+3\right)\)

6, \(x^3-\frac{1}{4}x=x\left(x^2-\frac{1}{4}\right)=x\left(x-\frac{1}{2}\right)\left(x+\frac{1}{2}\right)\)

7, \(2x-2y-x^2+2xy-y^2=\left(2x-2y\right)-\left(x^2-2xy+y^2\right)=2\left(x-y\right)-\left(x-y\right)^2=\left(x-y\right)\left(2-x+y\right)\)

8, \(\left(2x+3\right)^2-\left(x+1\right)^2=\left(2x+3+x+1\right)\left(2x+3-x-1\right)=\left(3x+4\right)\left(x+2\right)\)

Ghi đề thì ghi cho chính xác bạn ơi. Ghi mà cái hình ko ra cái j sao mà giải. tam giác mà 4 điểm ABCD lận à. Rồi DB là trung tuyến, tùm lum vậy!