Solve 3(-2n^{4}+n^3-7n+9)+(-4n-6+2n^3+10n^2-5n^4)

$$3 ( - 2 n ^ { 4 } + n ^ { 3 } - 7 n + 9 ) + ( - 4 n - 6 + 2 n ^ { 3 } + 10 n ^ { 2 } - 5 n ^ { 4 } )$$

Evaluate

$$\left(n-1\right)\left(-11n^{3}-6n^{2}+4n-21\right)$$

Solution Steps

Use the distributive property to multiply 3 by -2n^{4}+n^{3}-7n+9.

$$-6n^{4}+3n^{3}-21n+27-4n-6+2n^{3}+10n^{2}-5n^{4}$$

Combine -21n and -4n to get -25n.

$$-6n^{4}+3n^{3}-25n+27-6+2n^{3}+10n^{2}-5n^{4}$$

Subtract 6 from 27 to get 21.

$$-6n^{4}+3n^{3}-25n+21+2n^{3}+10n^{2}-5n^{4}$$

Combine 3n^{3} and 2n^{3} to get 5n^{3}.

$$-6n^{4}+5n^{3}-25n+21+10n^{2}-5n^{4}$$

Combine -6n^{4} and -5n^{4} to get -11n^{4}.

$$-11n^{4}+5n^{3}-25n+21+10n^{2}$$

Expand

$$21-25n+10n^{2}+5n^{3}-11n^{4}$$

Solution Steps

Use the distributive property to multiply 3 by -2n^{4}+n^{3}-7n+9.

$$-6n^{4}+3n^{3}-21n+27-4n-6+2n^{3}+10n^{2}-5n^{4}$$

Combine -21n and -4n to get -25n.

$$-6n^{4}+3n^{3}-25n+27-6+2n^{3}+10n^{2}-5n^{4}$$

Subtract 6 from 27 to get 21.

$$-6n^{4}+3n^{3}-25n+21+2n^{3}+10n^{2}-5n^{4}$$

Combine 3n^{3} and 2n^{3} to get 5n^{3}.

$$-6n^{4}+5n^{3}-25n+21+10n^{2}-5n^{4}$$

Combine -6n^{4} and -5n^{4} to get -11n^{4}.

$$-11n^{4}+5n^{3}-25n+21+10n^{2}$$