Question

Упростите выражение (a3 + b3)3 – (a3 – b3)3 – 2b9
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Answer 1

(a³+b³)³-(a³-b³)³-2b⁹= (a³+b³-a³+b³)(a⁶+2a³b³+b⁶+a⁶-b⁶+a⁶-2a³b³+b⁶)-2b⁹= 2b³(3a⁶+b⁶)-2b⁹= 6a⁶b³+2b⁹-2b⁹= 6a⁶b³

Answer 2

$\displaystyle \tt (a^3+b^3)^3-(a^3-b^3)^3-2b^9=a^9+3a^6b^3+3a^3b^6+b^9-(a^9-3a^6b^3+3a^3b^6-b^9)-2b^9=a^9+3a^6b^3+3a^3b^6-a^9+3a^6b^3-3a^3b^6+b^9-2b^9=\boxed{\bold{6a^6b^3}}$