Solve (5-a^3)^2

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

Expand

$$a^{6}-10a^{3}+25$$

Solution Steps

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

$$25-10a^{3}+\left(a^{3}\right)^{2}$$

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

$$25-10a^{3}+a^{6}$$

Evaluate

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

Solution Steps

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

$$25-10a^{3}+\left(a^{3}\right)^{2}$$

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

$$25-10a^{3}+a^{6}$$