Solve (3x-2y)(x-3y)+(x-4y)(x-10y)-(-x+6y)(7x+3y)

$$( 3 x - 2 y ) ( x - 3 y ) + ( x - 4 y ) ( x - 10 y ) - ( - x + 6 y ) ( 7 x + 3 y )$$

Evaluate

$$11x^{2}-64xy+28y^{2}$$

Solution Steps

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

$$3x^{2}-9xy-2yx+6y^{2}+\left(x-4y\right)\left(x-10y\right)-\left(-x+6y\right)\left(7x+3y\right)$$

Combine -9xy and -2yx to get -11xy.

$$3x^{2}-11xy+6y^{2}+\left(x-4y\right)\left(x-10y\right)-\left(-x+6y\right)\left(7x+3y\right)$$

Apply the distributive property by multiplying each term of x-4y by each term of x-10y.

$$3x^{2}-11xy+6y^{2}+x^{2}-10xy-4yx+40y^{2}-\left(-x+6y\right)\left(7x+3y\right)$$

Combine -10xy and -4yx to get -14xy.

$$3x^{2}-11xy+6y^{2}+x^{2}-14xy+40y^{2}-\left(-x+6y\right)\left(7x+3y\right)$$

Combine 3x^{2} and x^{2} to get 4x^{2}.

$$4x^{2}-11xy+6y^{2}-14xy+40y^{2}-\left(-x+6y\right)\left(7x+3y\right)$$

Combine -11xy and -14xy to get -25xy.

$$4x^{2}-25xy+6y^{2}+40y^{2}-\left(-x+6y\right)\left(7x+3y\right)$$

Combine 6y^{2} and 40y^{2} to get 46y^{2}.

$$4x^{2}-25xy+46y^{2}-\left(-x+6y\right)\left(7x+3y\right)$$

Apply the distributive property by multiplying each term of -x+6y by each term of 7x+3y.

$$4x^{2}-25xy+46y^{2}-\left(7\left(-x\right)x+3\left(-x\right)y+42yx+18y^{2}\right)$$

To find the opposite of 7\left(-x\right)x+3\left(-x\right)y+42yx+18y^{2}, find the opposite of each term.

$$4x^{2}-25xy+46y^{2}-7\left(-x\right)x-3\left(-x\right)y-42yx-18y^{2}$$

Multiply -7 and -1 to get 7.

$$4x^{2}-25xy+46y^{2}+7xx-3\left(-x\right)y-42yx-18y^{2}$$

Multiply x and x to get x^{2}.

$$4x^{2}-25xy+46y^{2}+7x^{2}-3\left(-x\right)y-42yx-18y^{2}$$

Combine 4x^{2} and 7x^{2} to get 11x^{2}.

$$11x^{2}-25xy+46y^{2}-3\left(-x\right)y-42yx-18y^{2}$$

Multiply -3 and -1 to get 3.

$$11x^{2}-25xy+46y^{2}+3xy-42yx-18y^{2}$$

Combine -25xy and 3xy to get -22xy.

$$11x^{2}-22xy+46y^{2}-42yx-18y^{2}$$

Combine -22xy and -42yx to get -64xy.

$$11x^{2}-64xy+46y^{2}-18y^{2}$$

Combine 46y^{2} and -18y^{2} to get 28y^{2}.

$$11x^{2}-64xy+28y^{2}$$

Expand

$$11x^{2}-64xy+28y^{2}$$

Solution Steps

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

$$3x^{2}-9xy-2yx+6y^{2}+\left(x-4y\right)\left(x-10y\right)-\left(-x+6y\right)\left(7x+3y\right)$$

Combine -9xy and -2yx to get -11xy.

$$3x^{2}-11xy+6y^{2}+\left(x-4y\right)\left(x-10y\right)-\left(-x+6y\right)\left(7x+3y\right)$$

Apply the distributive property by multiplying each term of x-4y by each term of x-10y.

$$3x^{2}-11xy+6y^{2}+x^{2}-10xy-4yx+40y^{2}-\left(-x+6y\right)\left(7x+3y\right)$$

Combine -10xy and -4yx to get -14xy.

$$3x^{2}-11xy+6y^{2}+x^{2}-14xy+40y^{2}-\left(-x+6y\right)\left(7x+3y\right)$$

Combine 3x^{2} and x^{2} to get 4x^{2}.

$$4x^{2}-11xy+6y^{2}-14xy+40y^{2}-\left(-x+6y\right)\left(7x+3y\right)$$

Combine -11xy and -14xy to get -25xy.

$$4x^{2}-25xy+6y^{2}+40y^{2}-\left(-x+6y\right)\left(7x+3y\right)$$

Combine 6y^{2} and 40y^{2} to get 46y^{2}.

$$4x^{2}-25xy+46y^{2}-\left(-x+6y\right)\left(7x+3y\right)$$

Apply the distributive property by multiplying each term of -x+6y by each term of 7x+3y.

$$4x^{2}-25xy+46y^{2}-\left(7\left(-x\right)x+3\left(-x\right)y+42yx+18y^{2}\right)$$

To find the opposite of 7\left(-x\right)x+3\left(-x\right)y+42yx+18y^{2}, find the opposite of each term.

$$4x^{2}-25xy+46y^{2}-7\left(-x\right)x-3\left(-x\right)y-42yx-18y^{2}$$

Multiply -7 and -1 to get 7.

$$4x^{2}-25xy+46y^{2}+7xx-3\left(-x\right)y-42yx-18y^{2}$$

Multiply x and x to get x^{2}.

$$4x^{2}-25xy+46y^{2}+7x^{2}-3\left(-x\right)y-42yx-18y^{2}$$

Combine 4x^{2} and 7x^{2} to get 11x^{2}.

$$11x^{2}-25xy+46y^{2}-3\left(-x\right)y-42yx-18y^{2}$$

Multiply -3 and -1 to get 3.

$$11x^{2}-25xy+46y^{2}+3xy-42yx-18y^{2}$$

Combine -25xy and 3xy to get -22xy.

$$11x^{2}-22xy+46y^{2}-42yx-18y^{2}$$

Combine -22xy and -42yx to get -64xy.

$$11x^{2}-64xy+46y^{2}-18y^{2}$$

Combine 46y^{2} and -18y^{2} to get 28y^{2}.

$$11x^{2}-64xy+28y^{2}$$