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6a^{3}-12a^{2}+9a-2a^{3}\left(3a+4\right)
Use the distributive property to multiply 3a by 2a^{2}-4a+3.
6a^{3}-12a^{2}+9a-6a^{4}-8a^{3}
Use the distributive property to multiply -2a^{3} by 3a+4.
-2a^{3}-12a^{2}+9a-6a^{4}
Combine 6a^{3} and -8a^{3} to get -2a^{3}.
6a^{3}-12a^{2}+9a-2a^{3}\left(3a+4\right)
Use the distributive property to multiply 3a by 2a^{2}-4a+3.
6a^{3}-12a^{2}+9a-6a^{4}-8a^{3}
Use the distributive property to multiply -2a^{3} by 3a+4.
-2a^{3}-12a^{2}+9a-6a^{4}
Combine 6a^{3} and -8a^{3} to get -2a^{3}.