Question

(a2+b2)(a4-a2b2+b4)-(a3-b3)(a3+b3)=2b6

Answer 1

(a²+b²)(a⁴-a²b²+b⁴)-(a³-b³)(a³+b³)=

(a²)³+(b²)³-(a³)²+(b³)²=

a^6+b^6-a^6+b^6=2b^6

Answer 2

$\underbrace {(a^2+b^2)(a^4-a^2b^2+b^4)}_{(a^2)^3+(b^2)^3}-\underbrace {(a^3-b^3)(a^3+b^3)}_{(a^3)^2-(b^3)^2}=\\\\=(a^2)^3+(b^2)^3-\Big ((a^3)^2-(b^3)^2\Big )=a^6+b^6-a^6+b^6=2b^6\\\\\\\star \; \; (x+y)^3=(x+y)(x^2-xy+y^2)\; \; \star \\\\\star \; \; (x-y)(x+y)=x^2-y^2\; \; \star$