a: \(64x^3-27y^3=\left(4x-3y\right)\left(16x^2+12xy+9y^2\right)\)
c: \(125-\left(x+1\right)^3\)
\(=\left(5-x-1\right)\left(25+5x+5+x^2+2x+1\right)\)
\(=\left(4-x\right)\left(x^2+7x+31\right)\)
a) \(64x^3-27y^3=\left(4x\right)^3-\left(3y\right)^3=\left(4x-3y\right)\left(16x^2+12xy+9y^2\right)\)
\(b)\) \(27x^3+\dfrac{y^3}{8}=\left(3x\right)^3+\left(\dfrac{y}{2}\right)^3\)
\(=\left(3x+\dfrac{y}{2}\right)\left(9x^2-\dfrac{3}{2}xy+\dfrac{1}{4}y^2\right)\)
\(c)\) \(125-\left(x+1\right)^3=5^3-\left(x+1\right)^3=\left(5-x-1\right)\left(25+5\left(x+1\right)+\left(x+1\right)^2\right)\)
\(=\left(4-x\right)\left(x^2+7x+31\right)\)