Solve 1/2xleft(3x+y-2right)*4+1/2xleft(2x-y+1right)*6

$$\frac{ 1 }{ 2 } x \left( 3x+y-2 \right) \times 4+ \frac{ 1 }{ 2 } x \left( 2x-y+1 \right) \times 6$$

Evaluate

$$x\left(12x-y-1\right)$$

Solution Steps

Multiply \frac{1}{2} and 4 to get \frac{4}{2}.

$$\frac{4}{2}x\left(3x+y-2\right)+\frac{1}{2}x\left(2x-y+1\right)\times 6$$

Divide 4 by 2 to get 2.

$$2x\left(3x+y-2\right)+\frac{1}{2}x\left(2x-y+1\right)\times 6$$

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

$$6x^{2}+2xy-4x+\frac{1}{2}x\left(2x-y+1\right)\times 6$$

Multiply \frac{1}{2} and 6 to get \frac{6}{2}.

$$6x^{2}+2xy-4x+\frac{6}{2}x\left(2x-y+1\right)$$

Divide 6 by 2 to get 3.

$$6x^{2}+2xy-4x+3x\left(2x-y+1\right)$$

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

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

Combine 6x^{2} and 6x^{2} to get 12x^{2}.

$$12x^{2}+2xy-4x-3xy+3x$$

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

$$12x^{2}-xy-4x+3x$$

Combine -4x and 3x to get -x.

$$12x^{2}-xy-x$$

Expand

$$12x^{2}-xy-x$$

Solution Steps

Multiply \frac{1}{2} and 4 to get \frac{4}{2}.

$$\frac{4}{2}x\left(3x+y-2\right)+\frac{1}{2}x\left(2x-y+1\right)\times 6$$

Divide 4 by 2 to get 2.

$$2x\left(3x+y-2\right)+\frac{1}{2}x\left(2x-y+1\right)\times 6$$

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

$$6x^{2}+2xy-4x+\frac{1}{2}x\left(2x-y+1\right)\times 6$$

Multiply \frac{1}{2} and 6 to get \frac{6}{2}.

$$6x^{2}+2xy-4x+\frac{6}{2}x\left(2x-y+1\right)$$

Divide 6 by 2 to get 3.

$$6x^{2}+2xy-4x+3x\left(2x-y+1\right)$$

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

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

Combine 6x^{2} and 6x^{2} to get 12x^{2}.

$$12x^{2}+2xy-4x-3xy+3x$$

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

$$12x^{2}-xy-4x+3x$$

Combine -4x and 3x to get -x.

$$12x^{2}-xy-x$$