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

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

Evaluate

$$y\left(y-9x\right)$$

Solution Steps

Use the distributive property to multiply 5x by x-y.

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

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

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

Combine -xy and 5yx to get 4xy.

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

To find the opposite of 5x^{2}+4xy-y^{2}, find the opposite of each term.

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

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

$$5x^{2}-5xy-5x^{2}-4xy+y^{2}$$

Combine 5x^{2} and -5x^{2} to get 0.

$$-5xy-4xy+y^{2}$$

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

$$-9xy+y^{2}$$

Expand

$$y^{2}-9xy$$

Solution Steps

Use the distributive property to multiply 5x by x-y.

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

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

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

Combine -xy and 5yx to get 4xy.

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

To find the opposite of 5x^{2}+4xy-y^{2}, find the opposite of each term.

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

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

$$5x^{2}-5xy-5x^{2}-4xy+y^{2}$$

Combine 5x^{2} and -5x^{2} to get 0.

$$-5xy-4xy+y^{2}$$

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

$$-9xy+y^{2}$$