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

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

Evaluate

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

Solution Steps

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

$$3x^{2}+5xy-9yx-15y^{2}-\left(3x+5y\right)\left(x+2y\right)$$

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

$$3x^{2}-4xy-15y^{2}-\left(3x+5y\right)\left(x+2y\right)$$

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

$$3x^{2}-4xy-15y^{2}-\left(3x^{2}+6xy+5yx+10y^{2}\right)$$

Combine 6xy and 5yx to get 11xy.

$$3x^{2}-4xy-15y^{2}-\left(3x^{2}+11xy+10y^{2}\right)$$

To find the opposite of 3x^{2}+11xy+10y^{2}, find the opposite of each term.

$$3x^{2}-4xy-15y^{2}-3x^{2}-11xy-10y^{2}$$

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

$$-4xy-15y^{2}-11xy-10y^{2}$$

Combine -4xy and -11xy to get -15xy.

$$-15xy-15y^{2}-10y^{2}$$

Combine -15y^{2} and -10y^{2} to get -25y^{2}.

$$-15xy-25y^{2}$$

Expand

$$-15xy-25y^{2}$$

Solution Steps

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

$$3x^{2}+5xy-9yx-15y^{2}-\left(3x+5y\right)\left(x+2y\right)$$

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

$$3x^{2}-4xy-15y^{2}-\left(3x+5y\right)\left(x+2y\right)$$

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

$$3x^{2}-4xy-15y^{2}-\left(3x^{2}+6xy+5yx+10y^{2}\right)$$

Combine 6xy and 5yx to get 11xy.

$$3x^{2}-4xy-15y^{2}-\left(3x^{2}+11xy+10y^{2}\right)$$

To find the opposite of 3x^{2}+11xy+10y^{2}, find the opposite of each term.

$$3x^{2}-4xy-15y^{2}-3x^{2}-11xy-10y^{2}$$

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

$$-4xy-15y^{2}-11xy-10y^{2}$$

Combine -4xy and -11xy to get -15xy.

$$-15xy-15y^{2}-10y^{2}$$

Combine -15y^{2} and -10y^{2} to get -25y^{2}.

$$-15xy-25y^{2}$$