If x+y+z = 8 and xy+yz+zx =20, find the value of x³ +y³ +z³ -3xyz.

If x = -2 and y = 1, by using an identity find the value of the following:

(i) (4y²–9x²) (16y⁴+36x²y²+81x⁴)

(ii)

(iii)

Find the following product:

(i) (3x+2y+2z) (9x²+4y²+4z²-6xy-4yz-6zx)

(ii) (4x-3y+2z) (16x²+9y²+4z²+12xy+6yz-8zx)

(iii) (2a-3b-2c) (4a²+9b²+4c²+6ab-6bc+4ca)

(iv) (3x-4y+5z)(9x²+16y²+25z²+12xy-15zx+20yz)

If a+b+c=9 and ab+bc+ca=26, find the value of a³ +b³ +c³ -3abc.

If a+b+c=9 and a²+b²+c²=35, find the value of a³ +b³ +c³ -3abc.