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

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

Evaluate

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

Solution Steps

Use the distributive property to multiply -y^{2}+x by x+y^{2}.

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

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

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

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

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

Expand

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

Solution Steps

Use the distributive property to multiply -y^{2}+x by x+y^{2}.

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

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

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

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

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