Resolve into linear factors `a^2+b^2+c^2-ab-bc-ca`

Resolve into linear factors: a^3-b^3

Resolve into linear factors: a^2-ab+b^2

Resolve into the linear factor: a^2+ab+b^2

Resolve into the linear factor: a^3+b^3

Resolve into the linear factor: a^3+b^3+c^3-3abc

ax^2+ by^2+ cz^2+2ayz+ 2bzx +2cxy can be resolved into linear factors if a, b, c are such that

Factorise : a^2 - ab - ca + bc

What should be subtracted from a^2+b^2+c^2-ab-bc-9 to get ab+bc+ca+abc+9

If 1, omega, omega^(2) are three cube roots of unity, show that (a + omega b+ omega^(2)c) (a + omega^(2)b+ omega c)= a^(2) + b^(2) + c^(2)- ab- bc - ca

Factorise : 4a^(2)+9b^(2)+16c^(2)+12ab-24bc-16ca