Question

factorise x⁶+3y⁶-z⁶+6x²y²z²​

Answer 1

Answer:

Consider, x6 + 3y6 – z6 + 6x2y2z2 = (x2)3 + (∛3 y2)3 +( –z2)3 – 3 (x2) (∛3y)2(– z2) It is in the form of a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 -ab - bc - ca) (x2)3 + (∛3 y2)3 +( –z2)3 – 3 (x2) (∛3y)2(– z2) = [(x2) + (∛3 y2) +( –z2)][(x2)2 + (∛3 y2)2 +( –z2)2 – x2(∛3 y2) – (∛3 y2)(– z2) – (– z2)x2 ] = [x2 + ∛3 y2 – z2)][ x4 + ∛9 y4 – z4 – x2(∛3 y2) + (∛3 y2)( z2) + z2x2 ]