Solve (8a^2-27)^3

$$( 8 a ^ { 2 } - 27 ) ^ { 3 }$$

Expand

$$512a^{6}-5184a^{4}+17496a^{2}-19683$$

Solution Steps

Use binomial theorem \left(p-q\right)^{3}=p^{3}-3p^{2}q+3pq^{2}-q^{3} to expand \left(8a^{2}-27\right)^{3}.

$$512\left(a^{2}\right)^{3}-5184\left(a^{2}\right)^{2}+17496a^{2}-19683$$

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

$$512a^{6}-5184\left(a^{2}\right)^{2}+17496a^{2}-19683$$

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

$$512a^{6}-5184a^{4}+17496a^{2}-19683$$

Evaluate

$$\left(8a^{2}-27\right)^{3}$$

Solution Steps

Use binomial theorem \left(p-q\right)^{3}=p^{3}-3p^{2}q+3pq^{2}-q^{3} to expand \left(8a^{2}-27\right)^{3}.

$$512\left(a^{2}\right)^{3}-5184\left(a^{2}\right)^{2}+17496a^{2}-19683$$

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

$$512a^{6}-5184\left(a^{2}\right)^{2}+17496a^{2}-19683$$

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

$$512a^{6}-5184a^{4}+17496a^{2}-19683$$