Solve (1/4-y^2)^2

$$( \frac { 1 } { 4 } - y ^ { 2 } ) ^ { 2 }$$

Evaluate

$$\frac{\left(1-4y^{2}\right)^{2}}{16}$$

Solution Steps

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

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

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

$$\frac{1}{16}-\frac{1}{2}y^{2}+y^{4}$$

Expand

$$y^{4}-\frac{y^{2}}{2}+\frac{1}{16}$$

Solution Steps

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

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

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

$$\frac{1}{16}-\frac{1}{2}y^{2}+y^{4}$$