Solve (4n^2-3)^3

$$( 4 n ^ { 2 } - 3 ) ^ { 3 }$$

Expand

$$64n^{6}-144n^{4}+108n^{2}-27$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(4n^{2}-3\right)^{3}.

$$64\left(n^{2}\right)^{3}-144\left(n^{2}\right)^{2}+108n^{2}-27$$

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

$$64n^{6}-144\left(n^{2}\right)^{2}+108n^{2}-27$$

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

$$64n^{6}-144n^{4}+108n^{2}-27$$

Evaluate

$$\left(4n^{2}-3\right)^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(4n^{2}-3\right)^{3}.

$$64\left(n^{2}\right)^{3}-144\left(n^{2}\right)^{2}+108n^{2}-27$$

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

$$64n^{6}-144\left(n^{2}\right)^{2}+108n^{2}-27$$

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

$$64n^{6}-144n^{4}+108n^{2}-27$$