Solve quad11x(2+y)-3(x+4y)-(4x+2xy+5)-9(xy+2)

$$\quad 11 x ( 2 + y ) - 3 ( x + 4 y ) - ( 4 x + 2 x y + 5 ) - 9 ( x y + 2 )$$

Evaluate

$$15x-12y-23$$

Solution Steps

Use the distributive property to multiply 11x by 2+y.

$$22x+11xy-3\left(x+4y\right)-\left(4x+2xy+5\right)-9\left(xy+2\right)$$

Use the distributive property to multiply -3 by x+4y.

$$22x+11xy-3x-12y-\left(4x+2xy+5\right)-9\left(xy+2\right)$$

Combine 22x and -3x to get 19x.

$$19x+11xy-12y-\left(4x+2xy+5\right)-9\left(xy+2\right)$$

To find the opposite of 4x+2xy+5, find the opposite of each term.

$$19x+11xy-12y-4x-2xy-5-9\left(xy+2\right)$$

Combine 19x and -4x to get 15x.

$$15x+11xy-12y-2xy-5-9\left(xy+2\right)$$

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

$$15x+9xy-12y-5-9\left(xy+2\right)$$

Use the distributive property to multiply -9 by xy+2.

$$15x+9xy-12y-5-9xy-18$$

Combine 9xy and -9xy to get 0.

$$15x-12y-5-18$$

Subtract 18 from -5 to get -23.

$$15x-12y-23$$

Expand

$$15x-12y-23$$

Solution Steps

Use the distributive property to multiply 11x by 2+y.

$$22x+11xy-3\left(x+4y\right)-\left(4x+2xy+5\right)-9\left(xy+2\right)$$

Use the distributive property to multiply -3 by x+4y.

$$22x+11xy-3x-12y-\left(4x+2xy+5\right)-9\left(xy+2\right)$$

Combine 22x and -3x to get 19x.

$$19x+11xy-12y-\left(4x+2xy+5\right)-9\left(xy+2\right)$$

To find the opposite of 4x+2xy+5, find the opposite of each term.

$$19x+11xy-12y-4x-2xy-5-9\left(xy+2\right)$$

Combine 19x and -4x to get 15x.

$$15x+11xy-12y-2xy-5-9\left(xy+2\right)$$

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

$$15x+9xy-12y-5-9\left(xy+2\right)$$

Use the distributive property to multiply -9 by xy+2.

$$15x+9xy-12y-5-9xy-18$$

Combine 9xy and -9xy to get 0.

$$15x-12y-5-18$$

Subtract 18 from -5 to get -23.

$$15x-12y-23$$