Solve (5-a^2)^3

$$( 5 - a ^ { 2 } ) ^ { 3 }$$

Expand

$$125-75a^{2}+15a^{4}-a^{6}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{3}=p^{3}-3p^{2}q+3pq^{2}-q^{3} to expand \left(5-a^{2}\right)^{3}.

$$125-75a^{2}+15\left(a^{2}\right)^{2}-\left(a^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$125-75a^{2}+15a^{4}-\left(a^{2}\right)^{3}$$

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

$$125-75a^{2}+15a^{4}-a^{6}$$

Evaluate

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

Solution Steps

Use binomial theorem \left(p-q\right)^{3}=p^{3}-3p^{2}q+3pq^{2}-q^{3} to expand \left(5-a^{2}\right)^{3}.

$$125-75a^{2}+15\left(a^{2}\right)^{2}-\left(a^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$125-75a^{2}+15a^{4}-\left(a^{2}\right)^{3}$$

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

$$125-75a^{2}+15a^{4}-a^{6}$$