Solve (4x^3-1)^3

$$( 4 x ^ { 3 } - 1 ) ^ { 3 }$$

Expand

$$64x^{9}-48x^{6}+12x^{3}-1$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(4x^{3}-1\right)^{3}.

$$64\left(x^{3}\right)^{3}-48\left(x^{3}\right)^{2}+12x^{3}-1$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$64x^{9}-48\left(x^{3}\right)^{2}+12x^{3}-1$$

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

$$64x^{9}-48x^{6}+12x^{3}-1$$

Evaluate

$$\left(4x^{3}-1\right)^{3}$$

Solution Steps

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(4x^{3}-1\right)^{3}.

$$64\left(x^{3}\right)^{3}-48\left(x^{3}\right)^{2}+12x^{3}-1$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$64x^{9}-48\left(x^{3}\right)^{2}+12x^{3}-1$$

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

$$64x^{9}-48x^{6}+12x^{3}-1$$