\(1,\\ \left(x-y\right)^2+\left(x+y\right)^2-2\left(x+y\right)\left(x-y\right)\\ =\left[\left(x-y\right)^2-2\left(x+y\right)\left(x-y\right)+\left(x+y\right)^2\right]\\ =\left[\left(x-y\right)-\left(x+y\right)\right]^2=\left[-2y\right]^2=4y^2\\ ---\\ 2,\left(5-x\right)^2+\left(x+5\right)^2-\left(2x+10\right)\left(x-5\right)\\ =\left(x-5\right)^2-2.\left(x+5\right)\left(x-5\right)+\left(x+5\right)^2\\ =\left[\left(x-5\right)-\left(x+5\right)\right]^2=\left[-10\right]^2=100\)
\(3,\left(x-2\right)^2+\left(x+1\right)^2+2\left(x-2\right)\left(-1-x\right)\\ =\left(x-2\right)^2-2\left(x-2\right)\left(x+1\right)+\left(x+1\right)^2\\ =\left[\left(x-2\right)-\left(x+1\right)\right]^2=\left[-3\right]^2=9\\ ---\\ 4,\left(2x+3y\right)^2+\left(2x-3y\right)^2-2\left(4x^2-9y^2\right)\\ =\left(2x+3y\right)^2-2.\left(2x+3y\right)\left(2x-3y\right)+\left(2x-3y\right)^2\\ =\left[\left(2x+3y\right)-\left(2x-3y\right)\right]^2\\ =\left[6y\right]^2=36y^2\)
3: \(\left(x-2\right)^2+\left(x+1\right)^2+2\left(x-2\right)\left(-1-x\right)\)
\(=\left(x-2\right)^2-2\left(x-2\right)\left(x+1\right)+\left(x+1\right)^2\)
\(=\left(x-2-x-1\right)^2=\left(-3\right)^2=9\)
4: \(\left(2x+3y\right)^2+\left(2x-3y\right)^2-2\left(4x^2-9y^2\right)\)
\(=\left(2x+3y\right)^2-2\left(2x+3y\right)\left(2x-3y\right)+\left(2x-3y\right)^2\)
\(=\left(2x+3y-2x+3y\right)^2=\left(6y\right)^2=36y^2\)
