Solve (x-2y)(2x+3y)-2(2y-x)(5x-y)

$$( x - 2 y ) ( 2 x + 3 y ) - 2 ( 2 y - x ) ( 5 x - y )$$

Evaluate

$$\left(x-2y\right)\left(12x+y\right)$$

Solution Steps

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

$$2x^{2}+3xy-4yx-6y^{2}-2\left(2y-x\right)\left(5x-y\right)$$

Combine 3xy and -4yx to get -xy.

$$2x^{2}-xy-6y^{2}-2\left(2y-x\right)\left(5x-y\right)$$

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

$$2x^{2}-xy-6y^{2}+\left(-4y+2x\right)\left(5x-y\right)$$

Apply the distributive property by multiplying each term of -4y+2x by each term of 5x-y.

$$2x^{2}-xy-6y^{2}-20yx+4y^{2}+10x^{2}-2xy$$

Combine -20yx and -2xy to get -22yx.

$$2x^{2}-xy-6y^{2}-22yx+4y^{2}+10x^{2}$$

Combine -xy and -22yx to get -23xy.

$$2x^{2}-23xy-6y^{2}+4y^{2}+10x^{2}$$

Combine -6y^{2} and 4y^{2} to get -2y^{2}.

$$2x^{2}-23xy-2y^{2}+10x^{2}$$

Combine 2x^{2} and 10x^{2} to get 12x^{2}.

$$12x^{2}-23xy-2y^{2}$$

Expand

$$12x^{2}-23xy-2y^{2}$$

Solution Steps

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

$$2x^{2}+3xy-4yx-6y^{2}-2\left(2y-x\right)\left(5x-y\right)$$

Combine 3xy and -4yx to get -xy.

$$2x^{2}-xy-6y^{2}-2\left(2y-x\right)\left(5x-y\right)$$

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

$$2x^{2}-xy-6y^{2}+\left(-4y+2x\right)\left(5x-y\right)$$

Apply the distributive property by multiplying each term of -4y+2x by each term of 5x-y.

$$2x^{2}-xy-6y^{2}-20yx+4y^{2}+10x^{2}-2xy$$

Combine -20yx and -2xy to get -22yx.

$$2x^{2}-xy-6y^{2}-22yx+4y^{2}+10x^{2}$$

Combine -xy and -22yx to get -23xy.

$$2x^{2}-23xy-6y^{2}+4y^{2}+10x^{2}$$

Combine -6y^{2} and 4y^{2} to get -2y^{2}.

$$2x^{2}-23xy-2y^{2}+10x^{2}$$

Combine 2x^{2} and 10x^{2} to get 12x^{2}.

$$12x^{2}-23xy-2y^{2}$$