Solve (10x+y)(3x+2y)-(5x-4y)(-x-6y)

$$( 10 x + y ) ( 3 x + 2 y ) - ( 5 x - 4 y ) ( - x - 6 y )$$

Evaluate

$$35x^{2}+49xy-22y^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 10x+y by each term of 3x+2y.

$$30x^{2}+20xy+3yx+2y^{2}-\left(5x-4y\right)\left(-x-6y\right)$$

Combine 20xy and 3yx to get 23xy.

$$30x^{2}+23xy+2y^{2}-\left(5x-4y\right)\left(-x-6y\right)$$

Apply the distributive property by multiplying each term of 5x-4y by each term of -x-6y.

$$30x^{2}+23xy+2y^{2}-\left(5x\left(-x\right)-30xy-4y\left(-x\right)+24y^{2}\right)$$

Multiply -4 and -1 to get 4.

$$30x^{2}+23xy+2y^{2}-\left(5x\left(-x\right)-30xy+4yx+24y^{2}\right)$$

Combine -30xy and 4yx to get -26xy.

$$30x^{2}+23xy+2y^{2}-\left(5x\left(-x\right)-26xy+24y^{2}\right)$$

To find the opposite of 5x\left(-x\right)-26xy+24y^{2}, find the opposite of each term.

$$30x^{2}+23xy+2y^{2}-5x\left(-x\right)-\left(-26xy\right)-24y^{2}$$

Multiply -5 and -1 to get 5.

$$30x^{2}+23xy+2y^{2}+5xx-\left(-26xy\right)-24y^{2}$$

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

$$30x^{2}+23xy+2y^{2}+5x^{2}-\left(-26xy\right)-24y^{2}$$

Combine 30x^{2} and 5x^{2} to get 35x^{2}.

$$35x^{2}+23xy+2y^{2}-\left(-26xy\right)-24y^{2}$$

The opposite of -26xy is 26xy.

$$35x^{2}+23xy+2y^{2}+26xy-24y^{2}$$

Combine 23xy and 26xy to get 49xy.

$$35x^{2}+49xy+2y^{2}-24y^{2}$$

Combine 2y^{2} and -24y^{2} to get -22y^{2}.

$$35x^{2}+49xy-22y^{2}$$

Expand

$$35x^{2}+49xy-22y^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 10x+y by each term of 3x+2y.

$$30x^{2}+20xy+3yx+2y^{2}-\left(5x-4y\right)\left(-x-6y\right)$$

Combine 20xy and 3yx to get 23xy.

$$30x^{2}+23xy+2y^{2}-\left(5x-4y\right)\left(-x-6y\right)$$

Apply the distributive property by multiplying each term of 5x-4y by each term of -x-6y.

$$30x^{2}+23xy+2y^{2}-\left(5x\left(-x\right)-30xy-4y\left(-x\right)+24y^{2}\right)$$

Multiply -4 and -1 to get 4.

$$30x^{2}+23xy+2y^{2}-\left(5x\left(-x\right)-30xy+4yx+24y^{2}\right)$$

Combine -30xy and 4yx to get -26xy.

$$30x^{2}+23xy+2y^{2}-\left(5x\left(-x\right)-26xy+24y^{2}\right)$$

To find the opposite of 5x\left(-x\right)-26xy+24y^{2}, find the opposite of each term.

$$30x^{2}+23xy+2y^{2}-5x\left(-x\right)-\left(-26xy\right)-24y^{2}$$

Multiply -5 and -1 to get 5.

$$30x^{2}+23xy+2y^{2}+5xx-\left(-26xy\right)-24y^{2}$$

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

$$30x^{2}+23xy+2y^{2}+5x^{2}-\left(-26xy\right)-24y^{2}$$

Combine 30x^{2} and 5x^{2} to get 35x^{2}.

$$35x^{2}+23xy+2y^{2}-\left(-26xy\right)-24y^{2}$$

The opposite of -26xy is 26xy.

$$35x^{2}+23xy+2y^{2}+26xy-24y^{2}$$

Combine 23xy and 26xy to get 49xy.

$$35x^{2}+49xy+2y^{2}-24y^{2}$$

Combine 2y^{2} and -24y^{2} to get -22y^{2}.

$$35x^{2}+49xy-22y^{2}$$