Solve (3a^3-5)^2

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

Expand

$$9a^{6}-30a^{3}+25$$

Solution Steps

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

$$9\left(a^{3}\right)^{2}-30a^{3}+25$$

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

$$9a^{6}-30a^{3}+25$$

Evaluate

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

Solution Steps

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

$$9\left(a^{3}\right)^{2}-30a^{3}+25$$

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

$$9a^{6}-30a^{3}+25$$