\(a,x^2-5x-y^2-5y=\left(x^2-y^2\right)-\left(5x+5y\right)=\left(x-y\right)\left(x+y\right)-5\left(x+y\right)=\left(x+y\right)\left(x-y-5\right)\\ b,x^3+2x^2-4x-8=\left(x^3+2x^2\right)-\left(4x+8\right)=x^2\left(x+2\right)-4\left(x+2\right)=\left(x^2-4\right)\left(x+2\right)=\left(x-2\right)\left(x+2\right)^2\\ c,a^3-8a^2+16a=a\left(a^2-8a+16\right)=a\left(a-4\right)^2\)
\(a,A=\left(x+3\right)^2+\left(x-2\right)^2-2\left(x+3\right)\left(x-2\right)\)
\(\Rightarrow A=\left(x+3-x-2\right)^2\)
\(\Rightarrow A=1^2\)
\(\Rightarrow A=1\)
\(b,B=\left(x-2\right)^3-x\left(x-1\right)\left(x-3\right)+3x^2-9x+8\)
\(\Rightarrow B=x^3-6x^2+12x-8-x\left(x^2-4x+3\right)+3x^2-9x+8\)
\(\Rightarrow B=x^3-3x^2+3x-x^3+4x^2-3x\)
\(\Rightarrow B=x^2\)
