Solve -(x-4x(3-2y))-3(-x(5y+1/3)+3xy)

$$- ( x - 4 x ( 3 - 2 y ) ) - 3 ( - x ( 5 y + \frac { 1 } { 3 } ) + 3 x y )$$

Evaluate

$$12x-2xy$$

Solution Steps

Use the distributive property to multiply -x by 5y+\frac{1}{3}.

$$-\left(x-4x\left(3-2y\right)\right)-3\left(5\left(-x\right)y+\left(-x\right)\times \frac{1}{3}+3xy\right)$$

Multiply -1 and 4 to get -4.

$$-\left(x-4x\left(3-2y\right)\right)-3\left(5\left(-1\right)xy-x\times \frac{1}{3}+3xy\right)$$

Use the distributive property to multiply -4x by 3-2y.

$$-\left(x-12x+8xy\right)-3\left(5\left(-1\right)xy-x\times \frac{1}{3}+3xy\right)$$

Combine x and -12x to get -11x.

$$-\left(-11x+8xy\right)-3\left(5\left(-1\right)xy-x\times \frac{1}{3}+3xy\right)$$

To find the opposite of -11x+8xy, find the opposite of each term.

$$-\left(-11x\right)-8xy-3\left(5\left(-1\right)xy-x\times \frac{1}{3}+3xy\right)$$

The opposite of -11x is 11x.

$$11x-8xy-3\left(5\left(-1\right)xy-x\times \frac{1}{3}+3xy\right)$$

Multiply 5 and -1 to get -5.

$$11x-8xy-3\left(-5xy-x\times \frac{1}{3}+3xy\right)$$

Multiply -1 and \frac{1}{3} to get -\frac{1}{3}.

$$11x-8xy-3\left(-5xy-\frac{1}{3}x+3xy\right)$$

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

$$11x-8xy-3\left(-2xy-\frac{1}{3}x\right)$$

Use the distributive property to multiply -3 by -2xy-\frac{1}{3}x.

$$11x-8xy+6xy-3\left(-\frac{1}{3}\right)x$$

Multiply -3 times -\frac{1}{3}.

$$11x-8xy+6xy+x$$

Combine -8xy and 6xy to get -2xy.

$$11x-2xy+x$$

Combine 11x and x to get 12x.

$$12x-2xy$$

Expand

$$12x-2xy$$

Solution Steps

Use the distributive property to multiply -x by 5y+\frac{1}{3}.

$$-\left(x-4x\left(3-2y\right)\right)-3\left(5\left(-x\right)y+\left(-x\right)\times \frac{1}{3}+3xy\right)$$

Multiply -1 and 4 to get -4.

$$-\left(x-4x\left(3-2y\right)\right)-3\left(5\left(-1\right)xy-x\times \frac{1}{3}+3xy\right)$$

Use the distributive property to multiply -4x by 3-2y.

$$-\left(x-12x+8xy\right)-3\left(5\left(-1\right)xy-x\times \frac{1}{3}+3xy\right)$$

Combine x and -12x to get -11x.

$$-\left(-11x+8xy\right)-3\left(5\left(-1\right)xy-x\times \frac{1}{3}+3xy\right)$$

To find the opposite of -11x+8xy, find the opposite of each term.

$$-\left(-11x\right)-8xy-3\left(5\left(-1\right)xy-x\times \frac{1}{3}+3xy\right)$$

The opposite of -11x is 11x.

$$11x-8xy-3\left(5\left(-1\right)xy-x\times \frac{1}{3}+3xy\right)$$

Multiply 5 and -1 to get -5.

$$11x-8xy-3\left(-5xy-x\times \frac{1}{3}+3xy\right)$$

Multiply -1 and \frac{1}{3} to get -\frac{1}{3}.

$$11x-8xy-3\left(-5xy-\frac{1}{3}x+3xy\right)$$

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

$$11x-8xy-3\left(-2xy-\frac{1}{3}x\right)$$

Use the distributive property to multiply -3 by -2xy-\frac{1}{3}x.

$$11x-8xy+6xy-3\left(-\frac{1}{3}\right)x$$

Multiply -3 times -\frac{1}{3}.

$$11x-8xy+6xy+x$$

Combine -8xy and 6xy to get -2xy.

$$11x-2xy+x$$

Combine 11x and x to get 12x.

$$12x-2xy$$