\(a,16x^2-4y^2\)
\(=\left(4x\right)^2-\left(2y\right)^2\)
\(=\left(4x-2y\right)\left(4x+2y\right)\)
\(=\left[2\left(2x-y\right)\right]\left[2\left(2x+y\right)\right]\)
\(=4\left(2x-y\right)\left(2x+y\right)\)
\(b,mx-my-nx+ny+y^2-2xy+x^2\)
\(=\left(mx-my\right)-\left(nx-ny\right)+\left(y^2-2xy+x^2\right)\)
\(=m\left(x-y\right)-n\left(x-y\right)+\left(x-y\right)^2\)
\(=\left(x-y\right)\left(m-n-x+y\right)\)
\(c,\left(x+y+z\right)^3-x^3-y^3-z^3\)
\(=\left[\left(x+y+z\right)^3-x^3\right]-\left[y^3+z^3\right]\)
\(=\left(x+y+z-x\right)\left[\left(x+y+z\right)^2+\left(x+y+z\right)x+x^2\right]-\left(y+z\right)\left(y^2-yz+z^2\right)\)
\(=\left(y+z\right)\left[\left(x+y+z\right)^2+x^2+xy+z^2-y^2+yz-z^2\right]\)
\(=\left(y+z\right)\left(x^2+y^2+z^2+2xy+2xz+2yz+x^2+xy+z^2-y^2+yz-z^2\right)\)
\(=\left(y+z\right)\left(2x^2+z^2+3xy+3yz+2xz\right)\)
