Solve (3/4a^2-8)^3

$$( \frac { 3 } { 4 } a ^ { 2 } - 8 ) ^ { 3 }$$

Evaluate

$$\frac{\left(3a^{2}-32\right)^{3}}{64}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{3}=p^{3}-3p^{2}q+3pq^{2}-q^{3} to expand \left(\frac{3}{4}a^{2}-8\right)^{3}.

$$\frac{27}{64}\left(a^{2}\right)^{3}-\frac{27}{2}\left(a^{2}\right)^{2}+144a^{2}-512$$

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

$$\frac{27}{64}a^{6}-\frac{27}{2}\left(a^{2}\right)^{2}+144a^{2}-512$$

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

$$\frac{27}{64}a^{6}-\frac{27}{2}a^{4}+144a^{2}-512$$

Expand

$$\frac{27a^{6}}{64}-\frac{27a^{4}}{2}+144a^{2}-512$$

Solution Steps

Use binomial theorem \left(p-q\right)^{3}=p^{3}-3p^{2}q+3pq^{2}-q^{3} to expand \left(\frac{3}{4}a^{2}-8\right)^{3}.

$$\frac{27}{64}\left(a^{2}\right)^{3}-\frac{27}{2}\left(a^{2}\right)^{2}+144a^{2}-512$$

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

$$\frac{27}{64}a^{6}-\frac{27}{2}\left(a^{2}\right)^{2}+144a^{2}-512$$

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

$$\frac{27}{64}a^{6}-\frac{27}{2}a^{4}+144a^{2}-512$$