Solve (x-2y)(2x-5y)+(3x-y)(4y-x)

$$(x-2y)(2x-5y)+(3x-y)(4y-x)$$

Evaluate

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

Solution Steps

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

$$2x^{2}-5xy-4yx+10y^{2}+\left(3x-y\right)\left(4y-x\right)$$

Combine -5xy and -4yx to get -9xy.

$$2x^{2}-9xy+10y^{2}+\left(3x-y\right)\left(4y-x\right)$$

Apply the distributive property by multiplying each term of 3x-y by each term of 4y-x.

$$2x^{2}-9xy+10y^{2}+12xy-3x^{2}-4y^{2}+yx$$

Combine 12xy and yx to get 13xy.

$$2x^{2}-9xy+10y^{2}+13xy-3x^{2}-4y^{2}$$

Combine -9xy and 13xy to get 4xy.

$$2x^{2}+4xy+10y^{2}-3x^{2}-4y^{2}$$

Combine 2x^{2} and -3x^{2} to get -x^{2}.

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

Combine 10y^{2} and -4y^{2} to get 6y^{2}.

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

Expand

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

Solution Steps

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

$$2x^{2}-5xy-4yx+10y^{2}+\left(3x-y\right)\left(4y-x\right)$$

Combine -5xy and -4yx to get -9xy.

$$2x^{2}-9xy+10y^{2}+\left(3x-y\right)\left(4y-x\right)$$

Apply the distributive property by multiplying each term of 3x-y by each term of 4y-x.

$$2x^{2}-9xy+10y^{2}+12xy-3x^{2}-4y^{2}+yx$$

Combine 12xy and yx to get 13xy.

$$2x^{2}-9xy+10y^{2}+13xy-3x^{2}-4y^{2}$$

Combine -9xy and 13xy to get 4xy.

$$2x^{2}+4xy+10y^{2}-3x^{2}-4y^{2}$$

Combine 2x^{2} and -3x^{2} to get -x^{2}.

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

Combine 10y^{2} and -4y^{2} to get 6y^{2}.

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