Solve [-(y^{4}-y^{2}+1)-(y^4+3y^2+1)]+(4y^4-6y^2-4)

$$[ - ( y ^ { 4 } - y ^ { 2 } + 1 ) - ( y ^ { 4 } + 3 y ^ { 2 } + 1 ) ] + ( 4 y ^ { 4 } - 6 y ^ { 2 } - 4 )$$

Evaluate

$$2\left(y^{4}-4y^{2}-3\right)$$

Solution Steps

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

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

To find the opposite of y^{4}+3y^{2}+1, find the opposite of each term.

$$-y^{4}+y^{2}-1-y^{4}-3y^{2}-1+4y^{4}-6y^{2}-4$$

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

$$-2y^{4}+y^{2}-1-3y^{2}-1+4y^{4}-6y^{2}-4$$

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

$$-2y^{4}-2y^{2}-1-1+4y^{4}-6y^{2}-4$$

Subtract 1 from -1 to get -2.

$$-2y^{4}-2y^{2}-2+4y^{4}-6y^{2}-4$$

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

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

Combine -2y^{2} and -6y^{2} to get -8y^{2}.

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

Subtract 4 from -2 to get -6.

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

Expand

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

Solution Steps

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

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

To find the opposite of y^{4}+3y^{2}+1, find the opposite of each term.

$$-y^{4}+y^{2}-1-y^{4}-3y^{2}-1+4y^{4}-6y^{2}-4$$

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

$$-2y^{4}+y^{2}-1-3y^{2}-1+4y^{4}-6y^{2}-4$$

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

$$-2y^{4}-2y^{2}-1-1+4y^{4}-6y^{2}-4$$

Subtract 1 from -1 to get -2.

$$-2y^{4}-2y^{2}-2+4y^{4}-6y^{2}-4$$

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

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

Combine -2y^{2} and -6y^{2} to get -8y^{2}.

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

Subtract 4 from -2 to get -6.

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