Solve (a^8-1)^3

$$( a ^ { 8 } - 1 ) ^ { 3 }$$

Expand

$$a^{24}-3a^{16}+3a^{8}-1$$

Solution Steps

Use binomial theorem \left(p-q\right)^{3}=p^{3}-3p^{2}q+3pq^{2}-q^{3} to expand \left(a^{8}-1\right)^{3}.

$$\left(a^{8}\right)^{3}-3\left(a^{8}\right)^{2}+3a^{8}-1$$

To raise a power to another power, multiply the exponents. Multiply 8 and 3 to get 24.

$$a^{24}-3\left(a^{8}\right)^{2}+3a^{8}-1$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$a^{24}-3a^{16}+3a^{8}-1$$

Evaluate

$$\left(a^{8}-1\right)^{3}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{3}=p^{3}-3p^{2}q+3pq^{2}-q^{3} to expand \left(a^{8}-1\right)^{3}.

$$\left(a^{8}\right)^{3}-3\left(a^{8}\right)^{2}+3a^{8}-1$$

To raise a power to another power, multiply the exponents. Multiply 8 and 3 to get 24.

$$a^{24}-3\left(a^{8}\right)^{2}+3a^{8}-1$$

To raise a power to another power, multiply the exponents. Multiply 8 and 2 to get 16.

$$a^{24}-3a^{16}+3a^{8}-1$$