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

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

Evaluate

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

Solution Steps

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

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

Use the distributive property to multiply x-x^{2} by -2x^{2}+x+1 and combine like terms.

$$-x^{2}+3x-1+2x^{4}-3x^{3}-3x^{3}+x+2x^{4}$$

Combine -3x^{3} and -3x^{3} to get -6x^{3}.

$$-x^{2}+3x-1+2x^{4}-6x^{3}+x+2x^{4}$$

Combine 3x and x to get 4x.

$$-x^{2}+4x-1+2x^{4}-6x^{3}+2x^{4}$$

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

$$-x^{2}+4x-1+4x^{4}-6x^{3}$$

Expand

$$4x^{4}-6x^{3}-x^{2}+4x-1$$

Solution Steps

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

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

Use the distributive property to multiply x-x^{2} by -2x^{2}+x+1 and combine like terms.

$$-x^{2}+3x-1+2x^{4}-3x^{3}-3x^{3}+x+2x^{4}$$

Combine -3x^{3} and -3x^{3} to get -6x^{3}.

$$-x^{2}+3x-1+2x^{4}-6x^{3}+x+2x^{4}$$

Combine 3x and x to get 4x.

$$-x^{2}+4x-1+2x^{4}-6x^{3}+2x^{4}$$

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

$$-x^{2}+4x-1+4x^{4}-6x^{3}$$