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

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

Evaluate

$$x^{4}$$

Solution Steps

Consider \left(x^{2}+y\right)\left(x^{2}-y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

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

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

Calculate -y to the power of 2 and get y^{2}.

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

Combine -y^{2} and y^{2} to get 0.

$$x^{4}$$

Expand

$$x^{4}$$

Solution Steps

Consider \left(x^{2}+y\right)\left(x^{2}-y\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

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

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

Calculate -y to the power of 2 and get y^{2}.

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

Combine -y^{2} and y^{2} to get 0.

$$x^{4}$$