Kesab Chandra Nag Solutions for Exercise 2: EXERCISE-2.2

Factorize the following polynomial: ${\mathrm{x}}^3+8{\mathrm{y}}^3+27{\mathrm{z}}^3-18\mathrm{xyz}$

Factorize the following polynomial: ${\mathrm{x}}^3-8{\mathrm{y}}^3+64{\mathrm{z}}^3+24\mathrm{xyz}$

Factorize the following polynomial: ${\left(\mathrm{x}-\mathrm{y}\right)}^3+{\left(\mathrm{y}-\mathrm{z}\right)}^3+{\left(\mathrm{z}-\mathrm{x}\right)}^3$

Factorize the following polynomial: ${\left(2\mathrm{a}-3\mathrm{b}\right)}^3+{\left(4\mathrm{c}-2\mathrm{a}\right)}^3+{\left(3\mathrm{b}-4\mathrm{c}\right)}^3$.

Factorize the following polynomial: ${\left(\frac{{\displaystyle \mathrm{x}}}{{\displaystyle 2}}+\mathrm{y}+\frac{\mathrm{z}}{3}\right)}^3+{\left(\frac{\mathrm{x}}{3}-\frac{2\mathrm{y}}{3}+\mathrm{z}\right)}^3-{\left(\frac{5\mathrm{x}}{6}+\frac{\mathrm{y}}{3}+\frac{4\mathrm{z}}{3}\right)}^3$

Factorize the following polynomial: ${\left(1-\mathrm{x}\right)}^3-{\left(1-\mathrm{y}\right)}^3+{\left(\mathrm{x}-\mathrm{y}\right)}^3$

Factorize the following polynomial: ${\left(5\mathrm{a}-7\mathrm{b}\right)}^3+{\left(9\mathrm{c}-5\mathrm{a}\right)}^3+{\left(7\mathrm{b}-9\mathrm{c}\right)}^3$

Factorize the following polynomial: ${\left(3\mathrm{a}-2\mathrm{b}\right)}^3+{\left(2\mathrm{b}-5\mathrm{c}\right)}^3+{\left(5\mathrm{c}-3\mathrm{a}\right)}^3$.