Solve y^{4}-6y^{5}+7y^{3}-8y-6-(3y^4-y^6+y^3+14-7y^2+4y

$$y ^ { 4 } - 6 y ^ { 5 } + 7 y ^ { 3 } - 8 y - 6 - ( 3 y ^ { 4 } - y ^ { 6 } + y ^ { 3 } + 14 - 7 y ^ { 2 } + 4 y$$

Evaluate

$$y^{6}-6y^{5}-2y^{4}+6y^{3}+7y^{2}-12y-20$$

Solution Steps

To find the opposite of 3y^{4}-y^{6}+y^{3}+14-7y^{2}+4y, find the opposite of each term.

$$y^{4}-6y^{5}+7y^{3}-8y-6-3y^{4}+y^{6}-y^{3}-14+7y^{2}-4y$$

Combine y^{4} and -3y^{4} to get -2y^{4}.

$$-2y^{4}-6y^{5}+7y^{3}-8y-6+y^{6}-y^{3}-14+7y^{2}-4y$$

Combine 7y^{3} and -y^{3} to get 6y^{3}.

$$-2y^{4}-6y^{5}+6y^{3}-8y-6+y^{6}-14+7y^{2}-4y$$

Subtract 14 from -6 to get -20.

$$-2y^{4}-6y^{5}+6y^{3}-8y-20+y^{6}+7y^{2}-4y$$

Combine -8y and -4y to get -12y.

$$-2y^{4}-6y^{5}+6y^{3}-12y-20+y^{6}+7y^{2}$$

Expand

$$y^{6}-6y^{5}-2y^{4}+6y^{3}+7y^{2}-12y-20$$

Solution Steps

To find the opposite of 3y^{4}-y^{6}+y^{3}+14-7y^{2}+4y, find the opposite of each term.

$$y^{4}-6y^{5}+7y^{3}-8y-6-3y^{4}+y^{6}-y^{3}-14+7y^{2}-4y$$

Combine y^{4} and -3y^{4} to get -2y^{4}.

$$-2y^{4}-6y^{5}+7y^{3}-8y-6+y^{6}-y^{3}-14+7y^{2}-4y$$

Combine 7y^{3} and -y^{3} to get 6y^{3}.

$$-2y^{4}-6y^{5}+6y^{3}-8y-6+y^{6}-14+7y^{2}-4y$$

Subtract 14 from -6 to get -20.

$$-2y^{4}-6y^{5}+6y^{3}-8y-20+y^{6}+7y^{2}-4y$$

Combine -8y and -4y to get -12y.

$$-2y^{4}-6y^{5}+6y^{3}-12y-20+y^{6}+7y^{2}$$