Solve [-(y^{4}-y^{2}+1)-(y^4+4y^2+1)]+(7y^4-3y^2-8)

$$[ - ( y ^ { 4 } - y ^ { 2 } + 1 ) - ( y ^ { 4 } + 4 y ^ { 2 } + 1 ) ] + ( 7 y ^ { 4 } - 3 y ^ { 2 } - 8 )$$

Evaluate

$$5y^{4}-6y^{2}-10$$

Solution Steps

To find the opposite of y^{4}-y^{2}+1, find the opposite of each term.

$$-y^{4}+y^{2}-1-\left(y^{4}+4y^{2}+1\right)+7y^{4}-3y^{2}-8$$

To find the opposite of y^{4}+4y^{2}+1, find the opposite of each term.

$$-y^{4}+y^{2}-1-y^{4}-4y^{2}-1+7y^{4}-3y^{2}-8$$

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

$$-2y^{4}+y^{2}-1-4y^{2}-1+7y^{4}-3y^{2}-8$$

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

$$-2y^{4}-3y^{2}-1-1+7y^{4}-3y^{2}-8$$

Subtract 1 from -1 to get -2.

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

Combine -2y^{4} and 7y^{4} to get 5y^{4}.

$$5y^{4}-3y^{2}-2-3y^{2}-8$$

Combine -3y^{2} and -3y^{2} to get -6y^{2}.

$$5y^{4}-6y^{2}-2-8$$

Subtract 8 from -2 to get -10.

$$5y^{4}-6y^{2}-10$$

Expand

$$5y^{4}-6y^{2}-10$$

Solution Steps

To find the opposite of y^{4}-y^{2}+1, find the opposite of each term.

$$-y^{4}+y^{2}-1-\left(y^{4}+4y^{2}+1\right)+7y^{4}-3y^{2}-8$$

To find the opposite of y^{4}+4y^{2}+1, find the opposite of each term.

$$-y^{4}+y^{2}-1-y^{4}-4y^{2}-1+7y^{4}-3y^{2}-8$$

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

$$-2y^{4}+y^{2}-1-4y^{2}-1+7y^{4}-3y^{2}-8$$

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

$$-2y^{4}-3y^{2}-1-1+7y^{4}-3y^{2}-8$$

Subtract 1 from -1 to get -2.

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

Combine -2y^{4} and 7y^{4} to get 5y^{4}.

$$5y^{4}-3y^{2}-2-3y^{2}-8$$

Combine -3y^{2} and -3y^{2} to get -6y^{2}.

$$5y^{4}-6y^{2}-2-8$$

Subtract 8 from -2 to get -10.

$$5y^{4}-6y^{2}-10$$