a) \(25\left(x-2\right)^2-16x^2\)
\(=\left[5\left(x-2\right)\right]^2-\left(4x\right)^2\)
\(=\left[5\left(x-2\right)-4x\right]\left[5\left(x-2\right)+4x\right]\)
\(=\left(5x-10-4x\right)\left(5x-10+4x\right)\)
\(=\left(x-10\right)\left(9x-10\right)\)
b) \(\left(2x-1\right)^3-8\)
\(=\left(2x-1\right)^3-2^3\)
\(=\left(2x-1-2\right)\left[\left(2x-1\right)^2+\left(2x-1\right)2+2^2\right]\)
\(=\left(2x-3\right)\left(4x^2-4x+1+4x-2+4\right)\)
\(=\left(2x-3\right)\left(4x^2+3\right)\)
c) \(\left(x^2+2\right)^2-6\left(x^2+2\right)+9\)
\(=\left(x^2+2\right)^2-2.\left(x^2+2\right).3+3^2\)
\(=\left(x^2+2-3\right)^2\)
\(=\left(x^2-1\right)^2\)
d) \(27x^3-\dfrac{1}{64}y^3\)
\(=\left(3x\right)^3-\left(\dfrac{1}{4}y\right)^3\)
\(=\left(3x-\dfrac{1}{4}y\right)\left[\left(3x\right)^2+3x.\dfrac{1}{4}y+\left(\dfrac{1}{4}y\right)^2\right]\)
\(=\left(3x-\dfrac{1}{4}y\right)\left(9x^2+\dfrac{3}{4}xy+\dfrac{1}{16}y^2\right)\)