\(a,=\left(x-8\right)^2=\left(8-8\right)^2=0\\ b,=\left(x-y-2z\right)\left(x-y+2z\right)\\ =\left(6+4-90\right)\left(6+4+90\right)=100\cdot\left(-80\right)=-8000\\ c,=\left(x+3\right)^3=\left(97+3\right)^3=1000000\\ d,=\left(3x-y\right)^3=\left(24-25\right)^3=-1\\ e,=\left(x-y\right)\left(x+y\right)\\ =\left(87-13\right)\left(87+13\right)=100\cdot74=7400\\ f,=\left(x+y\right)\left(x-1\right)\\ =\left(2000+1999\right)\left(2000-1\right)=3999\cdot1999=...\\ g,=\left(x+1-x-4\right)^2=9\)
a. \(x^2-16x+64=\left(x-8\right)^2=\left(8-8\right)^2=0\)
b. \(x^2-2xy-4z^2+y^2=\left(x-y\right)^2-\left(2z\right)^2=\left(x-y-2z\right)\left(x-y+2z\right)=\left(6+4-90\right)\left(6+4+90\right)=100.-80=-8000\)
c. \(x^3+9x^2+27x+27=\left(x+3\right)^3=\left(97+3\right)^3=1000000\)
d. \(27x^3-27x^2y+9xy^2-y^3=\left(3x-y\right)^3=\left(24-25\right)^3=-1\)
e. \(x^2-y^2=\left(x-y\right)\left(x+y\right)=\left(87-13\right)\left(87+13\right)=100.74=7400\)
f. \(x\left(x-1\right)-y\left(1-x\right)=\left(x+y\right)\left(x-1\right)=3999.1999=7994001\)
g. \(\left(x+1\right)^2+\left(x+4\right)^2-2\left(x+1\right)\left(x+4\right)=\left(x+1-x-4\right)^2=\left(-3\right)^2=9\)
