Solve (x^2-1)(-x^2+3)

$$( x ^ { 2 } - 1 ) ( - x ^ { 2 } + 3 )$$

Evaluate

$$-x^{4}+4x^{2}-3$$

Solution Steps

Use the distributive property to multiply x^{2}-1 by -x^{2}+3.

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

Multiply -1 and -1 to get 1.

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

Combine 3x^{2} and x^{2} to get 4x^{2}.

$$x^{2}\left(-x^{2}\right)+4x^{2}-3$$

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

$$x^{4}\left(-1\right)+4x^{2}-3$$

Expand

$$-x^{4}+4x^{2}-3$$

Solution Steps

Use the distributive property to multiply x^{2}-1 by -x^{2}+3.

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

Multiply -1 and -1 to get 1.

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

Combine 3x^{2} and x^{2} to get 4x^{2}.

$$x^{2}\left(-x^{2}\right)+4x^{2}-3$$

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

$$x^{4}\left(-1\right)+4x^{2}-3$$