Question

Answer 1

a: ta có; \(\left(2x-y\right)\left(4x^2+2xy+y^2\right)-\left(2x+y\right)\left(4x^2-2xy+y^2\right)\)

\(=\left(8x^3-y^3\right)-\left(8x^3+y^3\right)\)

\(=8x^3-y^3-8x^3-y^3=-2y^3\)

b: \(\left(x+y\right)^2-\left(2x+2y\right)\left(x-3y\right)+\left(x-3y\right)^2\)

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

\(=\left(x+y-x+3y\right)^2=\left(4y\right)^2=16y^2\)

c: \(\left(x+y+z\right)^2-\left(x+y-z\right)^2\)

\(=\left(x+y+z-x-y+z\right)\left(x+y+z+x+y-z\right)\)

\(=2z\cdot2\left(x+y\right)=4z\left(x+y\right)\)