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a^{3}-11a^{2}+7
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a^{3}-11a^{2}+7
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2a^{3}-8a^{2}-a+4-\left(a+3\right)\left(a^{2}-1\right)
Use the distributive property to multiply 2a^{2}-1 by a-4.
2a^{3}-8a^{2}-a+4-\left(a^{3}-a+3a^{2}-3\right)
Use the distributive property to multiply a+3 by a^{2}-1.
2a^{3}-8a^{2}-a+4-a^{3}+a-3a^{2}+3
To find the opposite of a^{3}-a+3a^{2}-3, find the opposite of each term.
a^{3}-8a^{2}-a+4+a-3a^{2}+3
Combine 2a^{3} and -a^{3} to get a^{3}.
a^{3}-8a^{2}+4-3a^{2}+3
Combine -a and a to get 0.
a^{3}-11a^{2}+4+3
Combine -8a^{2} and -3a^{2} to get -11a^{2}.
a^{3}-11a^{2}+7
Add 4 and 3 to get 7.
2a^{3}-8a^{2}-a+4-\left(a+3\right)\left(a^{2}-1\right)
Use the distributive property to multiply 2a^{2}-1 by a-4.
2a^{3}-8a^{2}-a+4-\left(a^{3}-a+3a^{2}-3\right)
Use the distributive property to multiply a+3 by a^{2}-1.
2a^{3}-8a^{2}-a+4-a^{3}+a-3a^{2}+3
To find the opposite of a^{3}-a+3a^{2}-3, find the opposite of each term.
a^{3}-8a^{2}-a+4+a-3a^{2}+3
Combine 2a^{3} and -a^{3} to get a^{3}.
a^{3}-8a^{2}+4-3a^{2}+3
Combine -a and a to get 0.
a^{3}-11a^{2}+4+3
Combine -8a^{2} and -3a^{2} to get -11a^{2}.
a^{3}-11a^{2}+7
Add 4 and 3 to get 7.
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