Solve (b^3+4)^3

$$( b ^ { 3 } + 4 ) ^ { 3 }$$

Expand

$$b^{9}+12b^{6}+48b^{3}+64$$

Solution Steps

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

$$\left(b^{3}\right)^{3}+12\left(b^{3}\right)^{2}+48b^{3}+64$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$b^{9}+12\left(b^{3}\right)^{2}+48b^{3}+64$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$b^{9}+12b^{6}+48b^{3}+64$$

Evaluate

$$\left(b^{3}+4\right)^{3}$$

Solution Steps

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

$$\left(b^{3}\right)^{3}+12\left(b^{3}\right)^{2}+48b^{3}+64$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$b^{9}+12\left(b^{3}\right)^{2}+48b^{3}+64$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$b^{9}+12b^{6}+48b^{3}+64$$