Solve (-1/5x+3/2y+2)(-1/2x-1/7y+6)

$$( - \frac { 1 } { 5 } x + \frac { 3 } { 2 } y + 2 ) ( - \frac { 1 } { 2 } x - \frac { 1 } { 7 } y + 6 )$$

Evaluate

$$\frac{\left(84-2y-7x\right)\left(20+15y-2x\right)}{140}$$

Solution Steps

Apply the distributive property by multiplying each term of -\frac{1}{5}x+\frac{3}{2}y+2 by each term of -\frac{1}{2}x-\frac{1}{7}y+6.

$$-\frac{1}{5}x\left(-\frac{1}{2}\right)x-\frac{1}{5}x\left(-\frac{1}{7}\right)y-\frac{1}{5}x\times 6+\frac{3}{2}y\left(-\frac{1}{2}\right)x+\frac{3}{2}y\left(-\frac{1}{7}\right)y+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

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

$$-\frac{1}{5}x^{2}\left(-\frac{1}{2}\right)-\frac{1}{5}x\left(-\frac{1}{7}\right)y-\frac{1}{5}x\times 6+\frac{3}{2}y\left(-\frac{1}{2}\right)x+\frac{3}{2}y\left(-\frac{1}{7}\right)y+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

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

$$-\frac{1}{5}x^{2}\left(-\frac{1}{2}\right)-\frac{1}{5}x\left(-\frac{1}{7}\right)y-\frac{1}{5}x\times 6+\frac{3}{2}y\left(-\frac{1}{2}\right)x+\frac{3}{2}y^{2}\left(-\frac{1}{7}\right)+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Multiply -\frac{1}{5} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(-1\right)}{5\times 2}x^{2}-\frac{1}{5}x\left(-\frac{1}{7}\right)y-\frac{1}{5}x\times 6+\frac{3}{2}y\left(-\frac{1}{2}\right)x+\frac{3}{2}y^{2}\left(-\frac{1}{7}\right)+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Do the multiplications in the fraction \frac{-\left(-1\right)}{5\times 2}.

$$\frac{1}{10}x^{2}-\frac{1}{5}x\left(-\frac{1}{7}\right)y-\frac{1}{5}x\times 6+\frac{3}{2}y\left(-\frac{1}{2}\right)x+\frac{3}{2}y^{2}\left(-\frac{1}{7}\right)+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Multiply -\frac{1}{5} times -\frac{1}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{10}x^{2}+\frac{-\left(-1\right)}{5\times 7}xy-\frac{1}{5}x\times 6+\frac{3}{2}y\left(-\frac{1}{2}\right)x+\frac{3}{2}y^{2}\left(-\frac{1}{7}\right)+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Do the multiplications in the fraction \frac{-\left(-1\right)}{5\times 7}.

$$\frac{1}{10}x^{2}+\frac{1}{35}xy-\frac{1}{5}x\times 6+\frac{3}{2}y\left(-\frac{1}{2}\right)x+\frac{3}{2}y^{2}\left(-\frac{1}{7}\right)+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Express -\frac{1}{5}\times 6 as a single fraction.

$$\frac{1}{10}x^{2}+\frac{1}{35}xy+\frac{-6}{5}x+\frac{3}{2}y\left(-\frac{1}{2}\right)x+\frac{3}{2}y^{2}\left(-\frac{1}{7}\right)+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Fraction \frac{-6}{5} can be rewritten as -\frac{6}{5} by extracting the negative sign.

$$\frac{1}{10}x^{2}+\frac{1}{35}xy-\frac{6}{5}x+\frac{3}{2}y\left(-\frac{1}{2}\right)x+\frac{3}{2}y^{2}\left(-\frac{1}{7}\right)+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Multiply \frac{3}{2} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{10}x^{2}+\frac{1}{35}xy-\frac{6}{5}x+\frac{3\left(-1\right)}{2\times 2}yx+\frac{3}{2}y^{2}\left(-\frac{1}{7}\right)+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Do the multiplications in the fraction \frac{3\left(-1\right)}{2\times 2}.

$$\frac{1}{10}x^{2}+\frac{1}{35}xy-\frac{6}{5}x+\frac{-3}{4}yx+\frac{3}{2}y^{2}\left(-\frac{1}{7}\right)+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$\frac{1}{10}x^{2}+\frac{1}{35}xy-\frac{6}{5}x-\frac{3}{4}yx+\frac{3}{2}y^{2}\left(-\frac{1}{7}\right)+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Combine \frac{1}{35}xy and -\frac{3}{4}yx to get -\frac{101}{140}xy.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{6}{5}x+\frac{3}{2}y^{2}\left(-\frac{1}{7}\right)+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Multiply \frac{3}{2} times -\frac{1}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{6}{5}x+\frac{3\left(-1\right)}{2\times 7}y^{2}+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Do the multiplications in the fraction \frac{3\left(-1\right)}{2\times 7}.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{6}{5}x+\frac{-3}{14}y^{2}+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Fraction \frac{-3}{14} can be rewritten as -\frac{3}{14} by extracting the negative sign.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{6}{5}x-\frac{3}{14}y^{2}+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Express \frac{3}{2}\times 6 as a single fraction.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{6}{5}x-\frac{3}{14}y^{2}+\frac{3\times 6}{2}y+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Multiply 3 and 6 to get 18.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{6}{5}x-\frac{3}{14}y^{2}+\frac{18}{2}y+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Divide 18 by 2 to get 9.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{6}{5}x-\frac{3}{14}y^{2}+9y+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Cancel out 2 and 2.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{6}{5}x-\frac{3}{14}y^{2}+9y-x+2\left(-\frac{1}{7}\right)y+12$$

Combine -\frac{6}{5}x and -x to get -\frac{11}{5}x.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{11}{5}x-\frac{3}{14}y^{2}+9y+2\left(-\frac{1}{7}\right)y+12$$

Express 2\left(-\frac{1}{7}\right) as a single fraction.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{11}{5}x-\frac{3}{14}y^{2}+9y+\frac{2\left(-1\right)}{7}y+12$$

Multiply 2 and -1 to get -2.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{11}{5}x-\frac{3}{14}y^{2}+9y+\frac{-2}{7}y+12$$

Fraction \frac{-2}{7} can be rewritten as -\frac{2}{7} by extracting the negative sign.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{11}{5}x-\frac{3}{14}y^{2}+9y-\frac{2}{7}y+12$$

Combine 9y and -\frac{2}{7}y to get \frac{61}{7}y.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{11}{5}x-\frac{3}{14}y^{2}+\frac{61}{7}y+12$$

Expand

$$-\frac{101xy}{140}+\frac{x^{2}}{10}-\frac{3y^{2}}{14}+\frac{61y}{7}-\frac{11x}{5}+12$$

Solution Steps

Apply the distributive property by multiplying each term of -\frac{1}{5}x+\frac{3}{2}y+2 by each term of -\frac{1}{2}x-\frac{1}{7}y+6.

$$-\frac{1}{5}x\left(-\frac{1}{2}\right)x-\frac{1}{5}x\left(-\frac{1}{7}\right)y-\frac{1}{5}x\times 6+\frac{3}{2}y\left(-\frac{1}{2}\right)x+\frac{3}{2}y\left(-\frac{1}{7}\right)y+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

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

$$-\frac{1}{5}x^{2}\left(-\frac{1}{2}\right)-\frac{1}{5}x\left(-\frac{1}{7}\right)y-\frac{1}{5}x\times 6+\frac{3}{2}y\left(-\frac{1}{2}\right)x+\frac{3}{2}y\left(-\frac{1}{7}\right)y+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

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

$$-\frac{1}{5}x^{2}\left(-\frac{1}{2}\right)-\frac{1}{5}x\left(-\frac{1}{7}\right)y-\frac{1}{5}x\times 6+\frac{3}{2}y\left(-\frac{1}{2}\right)x+\frac{3}{2}y^{2}\left(-\frac{1}{7}\right)+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Multiply -\frac{1}{5} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(-1\right)}{5\times 2}x^{2}-\frac{1}{5}x\left(-\frac{1}{7}\right)y-\frac{1}{5}x\times 6+\frac{3}{2}y\left(-\frac{1}{2}\right)x+\frac{3}{2}y^{2}\left(-\frac{1}{7}\right)+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Do the multiplications in the fraction \frac{-\left(-1\right)}{5\times 2}.

$$\frac{1}{10}x^{2}-\frac{1}{5}x\left(-\frac{1}{7}\right)y-\frac{1}{5}x\times 6+\frac{3}{2}y\left(-\frac{1}{2}\right)x+\frac{3}{2}y^{2}\left(-\frac{1}{7}\right)+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Multiply -\frac{1}{5} times -\frac{1}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{10}x^{2}+\frac{-\left(-1\right)}{5\times 7}xy-\frac{1}{5}x\times 6+\frac{3}{2}y\left(-\frac{1}{2}\right)x+\frac{3}{2}y^{2}\left(-\frac{1}{7}\right)+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Do the multiplications in the fraction \frac{-\left(-1\right)}{5\times 7}.

$$\frac{1}{10}x^{2}+\frac{1}{35}xy-\frac{1}{5}x\times 6+\frac{3}{2}y\left(-\frac{1}{2}\right)x+\frac{3}{2}y^{2}\left(-\frac{1}{7}\right)+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Express -\frac{1}{5}\times 6 as a single fraction.

$$\frac{1}{10}x^{2}+\frac{1}{35}xy+\frac{-6}{5}x+\frac{3}{2}y\left(-\frac{1}{2}\right)x+\frac{3}{2}y^{2}\left(-\frac{1}{7}\right)+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Fraction \frac{-6}{5} can be rewritten as -\frac{6}{5} by extracting the negative sign.

$$\frac{1}{10}x^{2}+\frac{1}{35}xy-\frac{6}{5}x+\frac{3}{2}y\left(-\frac{1}{2}\right)x+\frac{3}{2}y^{2}\left(-\frac{1}{7}\right)+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Multiply \frac{3}{2} times -\frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{10}x^{2}+\frac{1}{35}xy-\frac{6}{5}x+\frac{3\left(-1\right)}{2\times 2}yx+\frac{3}{2}y^{2}\left(-\frac{1}{7}\right)+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Do the multiplications in the fraction \frac{3\left(-1\right)}{2\times 2}.

$$\frac{1}{10}x^{2}+\frac{1}{35}xy-\frac{6}{5}x+\frac{-3}{4}yx+\frac{3}{2}y^{2}\left(-\frac{1}{7}\right)+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$\frac{1}{10}x^{2}+\frac{1}{35}xy-\frac{6}{5}x-\frac{3}{4}yx+\frac{3}{2}y^{2}\left(-\frac{1}{7}\right)+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Combine \frac{1}{35}xy and -\frac{3}{4}yx to get -\frac{101}{140}xy.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{6}{5}x+\frac{3}{2}y^{2}\left(-\frac{1}{7}\right)+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Multiply \frac{3}{2} times -\frac{1}{7} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{6}{5}x+\frac{3\left(-1\right)}{2\times 7}y^{2}+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Do the multiplications in the fraction \frac{3\left(-1\right)}{2\times 7}.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{6}{5}x+\frac{-3}{14}y^{2}+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Fraction \frac{-3}{14} can be rewritten as -\frac{3}{14} by extracting the negative sign.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{6}{5}x-\frac{3}{14}y^{2}+\frac{3}{2}y\times 6+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Express \frac{3}{2}\times 6 as a single fraction.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{6}{5}x-\frac{3}{14}y^{2}+\frac{3\times 6}{2}y+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Multiply 3 and 6 to get 18.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{6}{5}x-\frac{3}{14}y^{2}+\frac{18}{2}y+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Divide 18 by 2 to get 9.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{6}{5}x-\frac{3}{14}y^{2}+9y+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)y+12$$

Cancel out 2 and 2.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{6}{5}x-\frac{3}{14}y^{2}+9y-x+2\left(-\frac{1}{7}\right)y+12$$

Combine -\frac{6}{5}x and -x to get -\frac{11}{5}x.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{11}{5}x-\frac{3}{14}y^{2}+9y+2\left(-\frac{1}{7}\right)y+12$$

Express 2\left(-\frac{1}{7}\right) as a single fraction.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{11}{5}x-\frac{3}{14}y^{2}+9y+\frac{2\left(-1\right)}{7}y+12$$

Multiply 2 and -1 to get -2.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{11}{5}x-\frac{3}{14}y^{2}+9y+\frac{-2}{7}y+12$$

Fraction \frac{-2}{7} can be rewritten as -\frac{2}{7} by extracting the negative sign.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{11}{5}x-\frac{3}{14}y^{2}+9y-\frac{2}{7}y+12$$

Combine 9y and -\frac{2}{7}y to get \frac{61}{7}y.

$$\frac{1}{10}x^{2}-\frac{101}{140}xy-\frac{11}{5}x-\frac{3}{14}y^{2}+\frac{61}{7}y+12$$