Solve (y^{4}-6y^{5}+y^{2}+7y^{3}-8y-y^{2}-6)-(-3y^{4}-y^6-8y^3+19+9y^3-7y^2+4y-5)

$$( y ^ { 4 } - 6 y ^ { 5 } + y ^ { 2 } + 7 y ^ { 3 } - 8 y - y ^ { 2 } - 6 ) - ( - 3 y ^ { 4 } - y ^ { 6 } - 8 y ^ { 3 } + 19 + 9 y ^ { 3 } - 7 y ^ { 2 } + 4 y - 5 )$$

Evaluate

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

Solution Steps

Combine y^{2} and -y^{2} to get 0.

$$y^{4}-6y^{5}+7y^{3}-8y-6-\left(-3y^{4}-y^{6}-8y^{3}+19+9y^{3}-7y^{2}+4y-5\right)$$

Combine -8y^{3} and 9y^{3} to get y^{3}.

$$y^{4}-6y^{5}+7y^{3}-8y-6-\left(-3y^{4}-y^{6}+y^{3}+19-7y^{2}+4y-5\right)$$

Subtract 5 from 19 to get 14.

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

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 4y^{4}.

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

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

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

Subtract 14 from -6 to get -20.

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

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

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

Expand

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

Solution Steps

Combine y^{2} and -y^{2} to get 0.

$$y^{4}-6y^{5}+7y^{3}-8y-6-\left(-3y^{4}-y^{6}-8y^{3}+19+9y^{3}-7y^{2}+4y-5\right)$$

Combine -8y^{3} and 9y^{3} to get y^{3}.

$$y^{4}-6y^{5}+7y^{3}-8y-6-\left(-3y^{4}-y^{6}+y^{3}+19-7y^{2}+4y-5\right)$$

Subtract 5 from 19 to get 14.

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

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 4y^{4}.

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

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

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

Subtract 14 from -6 to get -20.

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

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

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