Solve ((a^2-a-6)*(a-4)-(a-9)*(a^2-2a-8))

$$( ( a ^ { 2 } - a - 6 ) \cdot ( a - 4 ) - ( a - 9 ) \cdot ( a ^ { 2 } - 2 a - 8 ) )$$

Evaluate

$$6\left(a-4\right)\left(a+2\right)$$

Solution Steps

Use the distributive property to multiply a^{2}-a-6 by a-4 and combine like terms.

$$a^{3}-5a^{2}-2a+24-\left(a-9\right)\left(a^{2}-2a-8\right)$$

Use the distributive property to multiply a-9 by a^{2}-2a-8 and combine like terms.

$$a^{3}-5a^{2}-2a+24-\left(a^{3}-11a^{2}+10a+72\right)$$

To find the opposite of a^{3}-11a^{2}+10a+72, find the opposite of each term.

$$a^{3}-5a^{2}-2a+24-a^{3}+11a^{2}-10a-72$$

Combine a^{3} and -a^{3} to get 0.

$$-5a^{2}-2a+24+11a^{2}-10a-72$$

Combine -5a^{2} and 11a^{2} to get 6a^{2}.

$$6a^{2}-2a+24-10a-72$$

Combine -2a and -10a to get -12a.

$$6a^{2}-12a+24-72$$

Subtract 72 from 24 to get -48.

$$6a^{2}-12a-48$$

Expand

$$6a^{2}-12a-48$$

Solution Steps

Use the distributive property to multiply a^{2}-a-6 by a-4 and combine like terms.

$$a^{3}-5a^{2}-2a+24-\left(a-9\right)\left(a^{2}-2a-8\right)$$

Use the distributive property to multiply a-9 by a^{2}-2a-8 and combine like terms.

$$a^{3}-5a^{2}-2a+24-\left(a^{3}-11a^{2}+10a+72\right)$$

To find the opposite of a^{3}-11a^{2}+10a+72, find the opposite of each term.

$$a^{3}-5a^{2}-2a+24-a^{3}+11a^{2}-10a-72$$

Combine a^{3} and -a^{3} to get 0.

$$-5a^{2}-2a+24+11a^{2}-10a-72$$

Combine -5a^{2} and 11a^{2} to get 6a^{2}.

$$6a^{2}-2a+24-10a-72$$

Combine -2a and -10a to get -12a.

$$6a^{2}-12a+24-72$$

Subtract 72 from 24 to get -48.

$$6a^{2}-12a-48$$