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

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

Evaluate

$$\left(1-x\right)\left(5x+6\right)$$

Solution Steps

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

$$2x^{2}-5x+3+\left(2-2x\right)\left(3x+1\right)+1-x^{2}$$

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

$$2x^{2}-5x+3+4x+2-6x^{2}+1-x^{2}$$

Combine -5x and 4x to get -x.

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

Add 3 and 2 to get 5.

$$2x^{2}-x+5-6x^{2}+1-x^{2}$$

Combine 2x^{2} and -6x^{2} to get -4x^{2}.

$$-4x^{2}-x+5+1-x^{2}$$

Add 5 and 1 to get 6.

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

Combine -4x^{2} and -x^{2} to get -5x^{2}.

$$-5x^{2}-x+6$$

Expand

$$6-x-5x^{2}$$

Solution Steps

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

$$2x^{2}-5x+3+\left(2-2x\right)\left(3x+1\right)+1-x^{2}$$

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

$$2x^{2}-5x+3+4x+2-6x^{2}+1-x^{2}$$

Combine -5x and 4x to get -x.

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

Add 3 and 2 to get 5.

$$2x^{2}-x+5-6x^{2}+1-x^{2}$$

Combine 2x^{2} and -6x^{2} to get -4x^{2}.

$$-4x^{2}-x+5+1-x^{2}$$

Add 5 and 1 to get 6.

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

Combine -4x^{2} and -x^{2} to get -5x^{2}.

$$-5x^{2}-x+6$$