Solve 4a^2-6a[7-a(6-a+a^2)]

$$4 a ^ { 2 } - 6 a [ 7 - a ( 6 - a + a ^ { 2 } ) ]$$

Evaluate

$$2a\left(3a^{3}-3a^{2}+20a-21\right)$$

Solution Steps

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

$$4a^{2}-6a\left(7-\left(6a-a^{2}+a^{3}\right)\right)$$

To find the opposite of 6a-a^{2}+a^{3}, find the opposite of each term.

$$4a^{2}-6a\left(7-6a+a^{2}-a^{3}\right)$$

Use the distributive property to multiply -6a by 7-6a+a^{2}-a^{3}.

$$4a^{2}-42a+36a^{2}-6a^{3}+6a^{4}$$

Combine 4a^{2} and 36a^{2} to get 40a^{2}.

$$40a^{2}-42a-6a^{3}+6a^{4}$$

Expand

$$6a^{4}-6a^{3}+40a^{2}-42a$$

Solution Steps

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

$$4a^{2}-6a\left(7-\left(6a-a^{2}+a^{3}\right)\right)$$

To find the opposite of 6a-a^{2}+a^{3}, find the opposite of each term.

$$4a^{2}-6a\left(7-6a+a^{2}-a^{3}\right)$$

Use the distributive property to multiply -6a by 7-6a+a^{2}-a^{3}.

$$4a^{2}-42a+36a^{2}-6a^{3}+6a^{4}$$

Combine 4a^{2} and 36a^{2} to get 40a^{2}.

$$40a^{2}-42a-6a^{3}+6a^{4}$$