Solve {l}{-4a^{4}-6a^3+2a^2}{-2a^2(2a^2+3a-1)}

$$\left. \begin{array} { l } { - 4 a ^ { 4 } - 6 a ^ { 3 } + 2 a ^ { 2 } } \\ { - 2 a ^ { 2 } ( 2 a ^ { 2 } + 3 a - 1 ) } \end{array} \right.$$

Evaluate

$$4a^{2}\left(1-3a-2a^{2}\right)$$

Solution Steps

Multiply -1 and 2 to get -2.

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

Use the distributive property to multiply -2a^{2} by 2a^{2}+3a-1.

$$-4a^{4}-6a^{3}+2a^{2}-4a^{4}-6a^{3}+2a^{2}$$

Combine -4a^{4} and -4a^{4} to get -8a^{4}.

$$-8a^{4}-6a^{3}+2a^{2}-6a^{3}+2a^{2}$$

Combine -6a^{3} and -6a^{3} to get -12a^{3}.

$$-8a^{4}-12a^{3}+2a^{2}+2a^{2}$$

Combine 2a^{2} and 2a^{2} to get 4a^{2}.

$$-8a^{4}-12a^{3}+4a^{2}$$

Expand

$$4a^{2}-12a^{3}-8a^{4}$$

Solution Steps

Multiply -1 and 2 to get -2.

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

Use the distributive property to multiply -2a^{2} by 2a^{2}+3a-1.

$$-4a^{4}-6a^{3}+2a^{2}-4a^{4}-6a^{3}+2a^{2}$$

Combine -4a^{4} and -4a^{4} to get -8a^{4}.

$$-8a^{4}-6a^{3}+2a^{2}-6a^{3}+2a^{2}$$

Combine -6a^{3} and -6a^{3} to get -12a^{3}.

$$-8a^{4}-12a^{3}+2a^{2}+2a^{2}$$

Combine 2a^{2} and 2a^{2} to get 4a^{2}.

$$-8a^{4}-12a^{3}+4a^{2}$$