Solve +a^{2}(-3a-10a^2)+3a(-a^2-4a-1)-2(-5a^4-6a^2-6a)=

$$+ a ^ { 2 } ( - 3 a - 10 a ^ { 2 } ) + 3 a ( - a ^ { 2 } - 4 a - 1 ) - 2 ( - 5 a ^ { 4 } - 6 a ^ { 2 } - 6 a ) =$$

Evaluate

$$9a-6a^{3}$$

Solution Steps

Use the distributive property to multiply a^{2} by -3a-10a^{2}.

$$-3a^{3}-10a^{4}+3a\left(-a^{2}-4a-1\right)-2\left(-5a^{4}-6a^{2}-6a\right)$$

Use the distributive property to multiply 3a by -a^{2}-4a-1.

$$-3a^{3}-10a^{4}+3a\left(-a^{2}\right)-12a^{2}-3a-2\left(-5a^{4}-6a^{2}-6a\right)$$

Use the distributive property to multiply -2 by -5a^{4}-6a^{2}-6a.

$$-3a^{3}-10a^{4}+3a\left(-a^{2}\right)-12a^{2}-3a+10a^{4}+12a^{2}+12a$$

Combine -10a^{4} and 10a^{4} to get 0.

$$-3a^{3}+3a\left(-a^{2}\right)-12a^{2}-3a+12a^{2}+12a$$

Combine -12a^{2} and 12a^{2} to get 0.

$$-3a^{3}+3a\left(-a^{2}\right)-3a+12a$$

Combine -3a and 12a to get 9a.

$$-3a^{3}+3a\left(-a^{2}\right)+9a$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$-3a^{3}+3a^{3}\left(-1\right)+9a$$

Multiply 3 and -1 to get -3.

$$-3a^{3}-3a^{3}+9a$$

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

$$-6a^{3}+9a$$

Expand

$$9a-6a^{3}$$

Solution Steps

Use the distributive property to multiply a^{2} by -3a-10a^{2}.

$$-3a^{3}-10a^{4}+3a\left(-a^{2}-4a-1\right)-2\left(-5a^{4}-6a^{2}-6a\right)$$

Use the distributive property to multiply 3a by -a^{2}-4a-1.

$$-3a^{3}-10a^{4}+3a\left(-a^{2}\right)-12a^{2}-3a-2\left(-5a^{4}-6a^{2}-6a\right)$$

Use the distributive property to multiply -2 by -5a^{4}-6a^{2}-6a.

$$-3a^{3}-10a^{4}+3a\left(-a^{2}\right)-12a^{2}-3a+10a^{4}+12a^{2}+12a$$

Combine -10a^{4} and 10a^{4} to get 0.

$$-3a^{3}+3a\left(-a^{2}\right)-12a^{2}-3a+12a^{2}+12a$$

Combine -12a^{2} and 12a^{2} to get 0.

$$-3a^{3}+3a\left(-a^{2}\right)-3a+12a$$

Combine -3a and 12a to get 9a.

$$-3a^{3}+3a\left(-a^{2}\right)+9a$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$-3a^{3}+3a^{3}\left(-1\right)+9a$$

Multiply 3 and -1 to get -3.

$$-3a^{3}-3a^{3}+9a$$

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

$$-6a^{3}+9a$$