1. c³*(2a+2b²)*(3a²-3ab²+3b⁴)=c³*2*(a+b²)*(3*(a²-ab²+b⁴)=6c³*(a³+b⁶).
2. 6c*(a⁶-b¹²)/(a²+ab²+b⁴)=6c*(a³-b⁶)*(a³+b⁶)/(a²+ab²+b⁴)=
=6c*(a-b²)*(a²+ab²+b⁴)*(a³+b⁶)/(a²+ab²+b⁴)=6c*(a-b²)*(a³+b⁶).
3. 6c*(a-b²)*(a³+b⁶)/6c³*(a³+c⁶)=(a-b²)/c².
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Answers & Comments
1. c³*(2a+2b²)*(3a²-3ab²+3b⁴)=c³*2*(a+b²)*(3*(a²-ab²+b⁴)=6c³*(a³+b⁶).
2. 6c*(a⁶-b¹²)/(a²+ab²+b⁴)=6c*(a³-b⁶)*(a³+b⁶)/(a²+ab²+b⁴)=
=6c*(a-b²)*(a²+ab²+b⁴)*(a³+b⁶)/(a²+ab²+b⁴)=6c*(a-b²)*(a³+b⁶).
3. 6c*(a-b²)*(a³+b⁶)/6c³*(a³+c⁶)=(a-b²)/c².