Solve (4x^3-1/4)^2

$$( 4 x ^ { 3 } - 1 / 4 ) ^ { 2 }$$

Evaluate

$$\frac{\left(16x^{3}-1\right)^{2}}{16}$$

Solution Steps

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

$$16\left(x^{3}\right)^{2}-2x^{3}+\frac{1}{16}$$

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

$$16x^{6}-2x^{3}+\frac{1}{16}$$

Expand

$$16x^{6}-2x^{3}+\frac{1}{16}$$

Solution Steps

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

$$16\left(x^{3}\right)^{2}-2x^{3}+\frac{1}{16}$$

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

$$16x^{6}-2x^{3}+\frac{1}{16}$$