Solve a(a^2-6a-9)-a(a^2-8a-15)+2a(3-a)

$$a ( a ^ { 2 } - 6 a - 9 ) - a ( a ^ { 2 } - 8 a - 15 ) + 2 a ( 3 - a )$$

Evaluate

$$12a$$

Solution Steps

Use the distributive property to multiply a by a^{2}-6a-9.

$$a^{3}-6a^{2}-9a-a\left(a^{2}-8a-15\right)+2a\left(3-a\right)$$

Use the distributive property to multiply a by a^{2}-8a-15.

$$a^{3}-6a^{2}-9a-\left(a^{3}-8a^{2}-15a\right)+2a\left(3-a\right)$$

To find the opposite of a^{3}-8a^{2}-15a, find the opposite of each term.

$$a^{3}-6a^{2}-9a-a^{3}+8a^{2}+15a+2a\left(3-a\right)$$

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

$$-6a^{2}-9a+8a^{2}+15a+2a\left(3-a\right)$$

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

$$2a^{2}-9a+15a+2a\left(3-a\right)$$

Combine -9a and 15a to get 6a.

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

Use the distributive property to multiply 2a by 3-a.

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

Combine 6a and 6a to get 12a.

$$2a^{2}+12a-2a^{2}$$

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

$$12a$$

Expand

$$12a$$

Solution Steps

Use the distributive property to multiply a by a^{2}-6a-9.

$$a^{3}-6a^{2}-9a-a\left(a^{2}-8a-15\right)+2a\left(3-a\right)$$

Use the distributive property to multiply a by a^{2}-8a-15.

$$a^{3}-6a^{2}-9a-\left(a^{3}-8a^{2}-15a\right)+2a\left(3-a\right)$$

To find the opposite of a^{3}-8a^{2}-15a, find the opposite of each term.

$$a^{3}-6a^{2}-9a-a^{3}+8a^{2}+15a+2a\left(3-a\right)$$

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

$$-6a^{2}-9a+8a^{2}+15a+2a\left(3-a\right)$$

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

$$2a^{2}-9a+15a+2a\left(3-a\right)$$

Combine -9a and 15a to get 6a.

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

Use the distributive property to multiply 2a by 3-a.

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

Combine 6a and 6a to get 12a.

$$2a^{2}+12a-2a^{2}$$

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

$$12a$$