Solve 4a^2-8a[6-a(8-a+a^2)]

$$4 a ^ { 2 } - 8 a [ 6 - a ( 8 - a + a ^ { 2 } ) ]$$

Evaluate

$$4a\left(2a^{3}-2a^{2}+17a-12\right)$$

Solution Steps

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

$$4a^{2}-8a\left(6-\left(8a-a^{2}+a^{3}\right)\right)$$

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

$$4a^{2}-8a\left(6-8a+a^{2}-a^{3}\right)$$

Use the distributive property to multiply -8a by 6-8a+a^{2}-a^{3}.

$$4a^{2}-48a+64a^{2}-8a^{3}+8a^{4}$$

Combine 4a^{2} and 64a^{2} to get 68a^{2}.

$$68a^{2}-48a-8a^{3}+8a^{4}$$

Expand

$$8a^{4}-8a^{3}+68a^{2}-48a$$

Solution Steps

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

$$4a^{2}-8a\left(6-\left(8a-a^{2}+a^{3}\right)\right)$$

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

$$4a^{2}-8a\left(6-8a+a^{2}-a^{3}\right)$$

Use the distributive property to multiply -8a by 6-8a+a^{2}-a^{3}.

$$4a^{2}-48a+64a^{2}-8a^{3}+8a^{4}$$

Combine 4a^{2} and 64a^{2} to get 68a^{2}.

$$68a^{2}-48a-8a^{3}+8a^{4}$$