Solve x^2+(y^2-4)^2-4

$$x ^ { 2 } + ( y ^ { 2 } - 4 ) ^ { 2 } - 4$$

Evaluate

$$\left(y^{2}-4\right)^{2}+x^{2}-4$$

Solution Steps

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

$$x^{2}+\left(y^{2}\right)^{2}-8y^{2}+16-4$$

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

$$x^{2}+y^{4}-8y^{2}+16-4$$

Subtract 4 from 16 to get 12.

$$x^{2}+y^{4}-8y^{2}+12$$

Expand

$$x^{2}+y^{4}-8y^{2}+12$$

Solution Steps

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

$$x^{2}+\left(y^{2}\right)^{2}-8y^{2}+16-4$$

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

$$x^{2}+y^{4}-8y^{2}+16-4$$

Subtract 4 from 16 to get 12.

$$x^{2}+y^{4}-8y^{2}+12$$