Solve x(2x-3y+1)-(4x^2+8xy-12x)/4

$$x ( 2 x - 3 y + 1 ) - \frac { ( 4 x ^ { 2 } + 8 x y - 12 x ) } { 4 }$$

Evaluate

$$x\left(x-5y+4\right)$$

Solution Steps

Divide each term of 4x^{2}+8xy-12x by 4 to get -3x+x^{2}+2xy.

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

To find the opposite of -3x+x^{2}+2xy, find the opposite of each term.

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

Use the distributive property to multiply x by 2x-3y+1.

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

Combine x and 3x to get 4x.

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

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

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

Combine -3xy and -2xy to get -5xy.

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

Expand

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

Solution Steps

Divide each term of 4x^{2}+8xy-12x by 4 to get -3x+x^{2}+2xy.

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

To find the opposite of -3x+x^{2}+2xy, find the opposite of each term.

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

Use the distributive property to multiply x by 2x-3y+1.

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

Combine x and 3x to get 4x.

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

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

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

Combine -3xy and -2xy to get -5xy.

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