`~rai~`
\(a)x^3+8\\=x^3+2^3\\=(x+2)(x^2-2x+4).\\b)27+y^3\\=3^3+y^3\\=(3+y)(9-3y+y^2).\\c)8a^3+125\\=(2a)^3+5^3\\=(2a+5)[(2a)^2-2a.5+5^2]\\=(2a+5)(4a^2-10a+25).\\d)64x^3+125y^3\\=(4x)^3+(5y)^3\\=(4x+5y)[(4x)^2-4x.5y+(5y)^2]\\=(4x+5y)(16x^2-20xy+25y^2).\\e)\dfrac{1}{27}x^3+\dfrac{1}{8}y^3\\=\left(\dfrac{1}{3}x\right)^3+\left(\dfrac{1}{2}y\right)^3\\=\left(\dfrac{1}{3}x+\dfrac{1}{2}y\right)\left[\left(\dfrac{1}{3}x\right)^2-\dfrac{1}{3}x.\dfrac{1}{2}y+\left(\dfrac{1}{2}y\right)^2\right]\\=\left(\dfrac{1}{3}x+\dfrac{1}{2}y\right)\left(\dfrac{1}{9}x^2-\dfrac{1}{6}xy+\dfrac{1}{4}y^2\right).\)
