Solve (-x^3+y)(x^3+y)

$$( - x ^ { 3 } + y ) ( x ^ { 3 } + y )$$

Evaluate

$$y^{2}-x^{6}$$

Solution Steps

Use the distributive property to multiply -x^{3}+y by x^{3}+y.

$$\left(-x^{3}\right)x^{3}+\left(-x^{3}\right)y+yx^{3}+y^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$-x^{6}-x^{3}y+yx^{3}+y^{2}$$

Combine -x^{3}y and yx^{3} to get 0.

$$-x^{6}+y^{2}$$

Expand

$$y^{2}-x^{6}$$

Solution Steps

Use the distributive property to multiply -x^{3}+y by x^{3}+y.

$$\left(-x^{3}\right)x^{3}+\left(-x^{3}\right)y+yx^{3}+y^{2}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$-x^{6}-x^{3}y+yx^{3}+y^{2}$$

Combine -x^{3}y and yx^{3} to get 0.

$$-x^{6}+y^{2}$$