Solve 3(y+1)(2-3x)-4(3x-2)(2y-1)

$$3 ( y + 1 ) ( 2 - 3 x ) - 4 ( 3 x - 2 ) ( 2 y - 1 )$$

Evaluate

$$\left(1-11y\right)\left(3x-2\right)$$

Solution Steps

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

$$\left(3y+3\right)\left(2-3x\right)-4\left(3x-2\right)\left(2y-1\right)$$

Apply the distributive property by multiplying each term of 3y+3 by each term of 2-3x.

$$6y-9yx+6-9x-4\left(3x-2\right)\left(2y-1\right)$$

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

$$6y-9yx+6-9x+\left(-12x+8\right)\left(2y-1\right)$$

Apply the distributive property by multiplying each term of -12x+8 by each term of 2y-1.

$$6y-9yx+6-9x-24xy+12x+16y-8$$

Combine -9yx and -24xy to get -33yx.

$$6y-33yx+6-9x+12x+16y-8$$

Combine -9x and 12x to get 3x.

$$6y-33yx+6+3x+16y-8$$

Combine 6y and 16y to get 22y.

$$22y-33yx+6+3x-8$$

Subtract 8 from 6 to get -2.

$$22y-33yx-2+3x$$

Expand

$$-33xy+3x+22y-2$$

Solution Steps

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

$$\left(3y+3\right)\left(2-3x\right)-4\left(3x-2\right)\left(2y-1\right)$$

Apply the distributive property by multiplying each term of 3y+3 by each term of 2-3x.

$$6y-9yx+6-9x-4\left(3x-2\right)\left(2y-1\right)$$

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

$$6y-9yx+6-9x+\left(-12x+8\right)\left(2y-1\right)$$

Apply the distributive property by multiplying each term of -12x+8 by each term of 2y-1.

$$6y-9yx+6-9x-24xy+12x+16y-8$$

Combine -9yx and -24xy to get -33yx.

$$6y-33yx+6-9x+12x+16y-8$$

Combine -9x and 12x to get 3x.

$$6y-33yx+6+3x+16y-8$$

Combine 6y and 16y to get 22y.

$$22y-33yx+6+3x-8$$

Subtract 8 from 6 to get -2.

$$22y-33yx-2+3x$$