Question

guys please help me
please resolve into factor this polynomial
a^6b^6 + b^6c^6 + c^6a^6

Answer 1

a^6b^6 + b^6c^6 + c^6a^6

→ (ab)^6 + (bc)^6 + (ac)^6

→ {(ab)³}² + {(bc)³}² + {(ac)³}²

★(x+y+z)² = x²+y²+z²+2(xy+yz+xz)

x²+y²+z² = (x+y+z)² – 2(xy+yz+xz)

→ {(ab)³}² + {(bc)³}² + {(ac)³}²

→ {(ab)³+(bc)³+(ac)³}² – 2{(ab)³(bc)³ + (bc)³(ac)³ + (ab)³(ac)³}

→ {(ab)³+(bc)³+(ac)³}² – 2{(ab²c)³ + (abc²)³ + (a²bc)³}

→ {(ab)³+(bc)³+(ac)³}² – 2{a³b^6c³ + a³b³c^6 + a^6b³c³}

→ {(ab)³+(bc)³+(ac)³}² – 2a³b^6c³ + 2a³b³c^6 + 2a^6b³c³

Hope it helps...