Solve (x-1)(x-3)-(4-x)(2x+1)-3x^2+2x-5

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

Evaluate

$$-9x-6$$

Solution Steps

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

$$x^{2}-4x+3-\left(4-x\right)\left(2x+1\right)-3x^{2}+2x-5$$

Use the distributive property to multiply 4-x by 2x+1 and combine like terms.

$$x^{2}-4x+3-\left(7x+4-2x^{2}\right)-3x^{2}+2x-5$$

To find the opposite of 7x+4-2x^{2}, find the opposite of each term.

$$x^{2}-4x+3-7x-4+2x^{2}-3x^{2}+2x-5$$

Combine -4x and -7x to get -11x.

$$x^{2}-11x+3-4+2x^{2}-3x^{2}+2x-5$$

Subtract 4 from 3 to get -1.

$$x^{2}-11x-1+2x^{2}-3x^{2}+2x-5$$

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

$$3x^{2}-11x-1-3x^{2}+2x-5$$

Combine 3x^{2} and -3x^{2} to get 0.

$$-11x-1+2x-5$$

Combine -11x and 2x to get -9x.

$$-9x-1-5$$

Subtract 5 from -1 to get -6.

$$-9x-6$$

Expand

$$-9x-6$$

Solution Steps

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

$$x^{2}-4x+3-\left(4-x\right)\left(2x+1\right)-3x^{2}+2x-5$$

Use the distributive property to multiply 4-x by 2x+1 and combine like terms.

$$x^{2}-4x+3-\left(7x+4-2x^{2}\right)-3x^{2}+2x-5$$

To find the opposite of 7x+4-2x^{2}, find the opposite of each term.

$$x^{2}-4x+3-7x-4+2x^{2}-3x^{2}+2x-5$$

Combine -4x and -7x to get -11x.

$$x^{2}-11x+3-4+2x^{2}-3x^{2}+2x-5$$

Subtract 4 from 3 to get -1.

$$x^{2}-11x-1+2x^{2}-3x^{2}+2x-5$$

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

$$3x^{2}-11x-1-3x^{2}+2x-5$$

Combine 3x^{2} and -3x^{2} to get 0.

$$-11x-1+2x-5$$

Combine -11x and 2x to get -9x.

$$-9x-1-5$$

Subtract 5 from -1 to get -6.

$$-9x-6$$