Solve a(8a-3)^2-(4a-1)^3+4

$$a ( 8 a - 3 ) ^ { 2 } - ( 4 a - 1 ) ^ { 3 } + 4$$

Evaluate

$$5-3a$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(8a-3\right)^{2}.

$$a\left(64a^{2}-48a+9\right)-\left(4a-1\right)^{3}+4$$

Use the distributive property to multiply a by 64a^{2}-48a+9.

$$64a^{3}-48a^{2}+9a-\left(4a-1\right)^{3}+4$$

Use binomial theorem \left(p-q\right)^{3}=p^{3}-3p^{2}q+3pq^{2}-q^{3} to expand \left(4a-1\right)^{3}.

$$64a^{3}-48a^{2}+9a-\left(64a^{3}-48a^{2}+12a-1\right)+4$$

To find the opposite of 64a^{3}-48a^{2}+12a-1, find the opposite of each term.

$$64a^{3}-48a^{2}+9a-64a^{3}+48a^{2}-12a+1+4$$

Combine 64a^{3} and -64a^{3} to get 0.

$$-48a^{2}+9a+48a^{2}-12a+1+4$$

Combine -48a^{2} and 48a^{2} to get 0.

$$9a-12a+1+4$$

Combine 9a and -12a to get -3a.

$$-3a+1+4$$

Add 1 and 4 to get 5.

$$-3a+5$$

Expand

$$5-3a$$

Solution Steps

Use binomial theorem \left(p-q\right)^{2}=p^{2}-2pq+q^{2} to expand \left(8a-3\right)^{2}.

$$a\left(64a^{2}-48a+9\right)-\left(4a-1\right)^{3}+4$$

Use the distributive property to multiply a by 64a^{2}-48a+9.

$$64a^{3}-48a^{2}+9a-\left(4a-1\right)^{3}+4$$

Use binomial theorem \left(p-q\right)^{3}=p^{3}-3p^{2}q+3pq^{2}-q^{3} to expand \left(4a-1\right)^{3}.

$$64a^{3}-48a^{2}+9a-\left(64a^{3}-48a^{2}+12a-1\right)+4$$

To find the opposite of 64a^{3}-48a^{2}+12a-1, find the opposite of each term.

$$64a^{3}-48a^{2}+9a-64a^{3}+48a^{2}-12a+1+4$$

Combine 64a^{3} and -64a^{3} to get 0.

$$-48a^{2}+9a+48a^{2}-12a+1+4$$

Combine -48a^{2} and 48a^{2} to get 0.

$$9a-12a+1+4$$

Combine 9a and -12a to get -3a.

$$-3a+1+4$$

Add 1 and 4 to get 5.

$$-3a+5$$