Solve 4n^{3}*(2n-3n^{2}+1)-3n^{2}*(4-3n^3-2n)+4n^2*(3n^3-1-4n-2n^2)=

$$4 n ^ { 3 } \cdot ( 2 n - 3 n ^ { 2 } + 1 ) - 3 n ^ { 2 } \cdot ( 4 - 3 n ^ { 3 } - 2 n ) + 4 n ^ { 2 } \cdot ( 3 n ^ { 3 } - 1 - 4 n - 2 n ^ { 2 } ) =$$

Evaluate

$$n^{2}\left(9n^{3}-6n-16\right)$$

Solution Steps

Use the distributive property to multiply 4n^{3} by 2n-3n^{2}+1.

$$8n^{4}-12n^{5}+4n^{3}-3n^{2}\left(4-3n^{3}-2n\right)+4n^{2}\left(3n^{3}-1-4n-2n^{2}\right)$$

Use the distributive property to multiply 4n^{2} by 3n^{3}-1-4n-2n^{2}.

$$8n^{4}-12n^{5}+4n^{3}-3n^{2}\left(4-3n^{3}-2n\right)+12n^{5}-4n^{2}-16n^{3}-8n^{4}$$

Use the distributive property to multiply -3n^{2} by 4-3n^{3}-2n.

$$8n^{4}-12n^{5}+4n^{3}-12n^{2}+9n^{5}+6n^{3}+12n^{5}-4n^{2}-16n^{3}-8n^{4}$$

Combine -12n^{5} and 9n^{5} to get -3n^{5}.

$$8n^{4}-3n^{5}+4n^{3}-12n^{2}+6n^{3}+12n^{5}-4n^{2}-16n^{3}-8n^{4}$$

Combine 4n^{3} and 6n^{3} to get 10n^{3}.

$$8n^{4}-3n^{5}+10n^{3}-12n^{2}+12n^{5}-4n^{2}-16n^{3}-8n^{4}$$

Combine -3n^{5} and 12n^{5} to get 9n^{5}.

$$8n^{4}+9n^{5}+10n^{3}-12n^{2}-4n^{2}-16n^{3}-8n^{4}$$

Combine -12n^{2} and -4n^{2} to get -16n^{2}.

$$8n^{4}+9n^{5}+10n^{3}-16n^{2}-16n^{3}-8n^{4}$$

Combine 10n^{3} and -16n^{3} to get -6n^{3}.

$$8n^{4}+9n^{5}-6n^{3}-16n^{2}-8n^{4}$$

Combine 8n^{4} and -8n^{4} to get 0.

$$9n^{5}-6n^{3}-16n^{2}$$

Expand

$$9n^{5}-6n^{3}-16n^{2}$$

Solution Steps

Use the distributive property to multiply 4n^{3} by 2n-3n^{2}+1.

$$8n^{4}-12n^{5}+4n^{3}-3n^{2}\left(4-3n^{3}-2n\right)+4n^{2}\left(3n^{3}-1-4n-2n^{2}\right)$$

Use the distributive property to multiply 4n^{2} by 3n^{3}-1-4n-2n^{2}.

$$8n^{4}-12n^{5}+4n^{3}-3n^{2}\left(4-3n^{3}-2n\right)+12n^{5}-4n^{2}-16n^{3}-8n^{4}$$

Use the distributive property to multiply -3n^{2} by 4-3n^{3}-2n.

$$8n^{4}-12n^{5}+4n^{3}-12n^{2}+9n^{5}+6n^{3}+12n^{5}-4n^{2}-16n^{3}-8n^{4}$$

Combine -12n^{5} and 9n^{5} to get -3n^{5}.

$$8n^{4}-3n^{5}+4n^{3}-12n^{2}+6n^{3}+12n^{5}-4n^{2}-16n^{3}-8n^{4}$$

Combine 4n^{3} and 6n^{3} to get 10n^{3}.

$$8n^{4}-3n^{5}+10n^{3}-12n^{2}+12n^{5}-4n^{2}-16n^{3}-8n^{4}$$

Combine -3n^{5} and 12n^{5} to get 9n^{5}.

$$8n^{4}+9n^{5}+10n^{3}-12n^{2}-4n^{2}-16n^{3}-8n^{4}$$

Combine -12n^{2} and -4n^{2} to get -16n^{2}.

$$8n^{4}+9n^{5}+10n^{3}-16n^{2}-16n^{3}-8n^{4}$$

Combine 10n^{3} and -16n^{3} to get -6n^{3}.

$$8n^{4}+9n^{5}-6n^{3}-16n^{2}-8n^{4}$$

Combine 8n^{4} and -8n^{4} to get 0.

$$9n^{5}-6n^{3}-16n^{2}$$