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

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

Evaluate

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

Solution Steps

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

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

To find the opposite of 4a-a^{2}+a^{3}, find the opposite of each term.

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

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

$$4a^{2}-16a+16a^{2}-4a^{3}+4a^{4}$$

Combine 4a^{2} and 16a^{2} to get 20a^{2}.

$$20a^{2}-16a-4a^{3}+4a^{4}$$

Expand

$$4a^{4}-4a^{3}+20a^{2}-16a$$

Solution Steps

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

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

To find the opposite of 4a-a^{2}+a^{3}, find the opposite of each term.

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

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

$$4a^{2}-16a+16a^{2}-4a^{3}+4a^{4}$$

Combine 4a^{2} and 16a^{2} to get 20a^{2}.

$$20a^{2}-16a-4a^{3}+4a^{4}$$