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

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

Evaluate

$$x\left(5x-3y\right)$$

Solution Steps

Apply the distributive property by multiplying each term of 2x+y by each term of 5x-3y.

$$10x^{2}-6xy+5yx-3y^{2}-\left(x+y\right)\left(5x-3y\right)$$

Combine -6xy and 5yx to get -xy.

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

Apply the distributive property by multiplying each term of x+y by each term of 5x-3y.

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

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

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

To find the opposite of 5x^{2}+2xy-3y^{2}, find the opposite of each term.

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

The opposite of -3y^{2} is 3y^{2}.

$$10x^{2}-xy-3y^{2}-5x^{2}-2xy+3y^{2}$$

Combine 10x^{2} and -5x^{2} to get 5x^{2}.

$$5x^{2}-xy-3y^{2}-2xy+3y^{2}$$

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

$$5x^{2}-3xy-3y^{2}+3y^{2}$$

Combine -3y^{2} and 3y^{2} to get 0.

$$5x^{2}-3xy$$

Expand

$$5x^{2}-3xy$$

Solution Steps

Apply the distributive property by multiplying each term of 2x+y by each term of 5x-3y.

$$10x^{2}-6xy+5yx-3y^{2}-\left(x+y\right)\left(5x-3y\right)$$

Combine -6xy and 5yx to get -xy.

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

Apply the distributive property by multiplying each term of x+y by each term of 5x-3y.

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

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

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

To find the opposite of 5x^{2}+2xy-3y^{2}, find the opposite of each term.

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

The opposite of -3y^{2} is 3y^{2}.

$$10x^{2}-xy-3y^{2}-5x^{2}-2xy+3y^{2}$$

Combine 10x^{2} and -5x^{2} to get 5x^{2}.

$$5x^{2}-xy-3y^{2}-2xy+3y^{2}$$

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

$$5x^{2}-3xy-3y^{2}+3y^{2}$$

Combine -3y^{2} and 3y^{2} to get 0.

$$5x^{2}-3xy$$