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

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

Evaluate

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

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}.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$\frac{1}{10}x^{2}+\frac{1}{35}x-\frac{3}{4}yx+\frac{-3}{14}y+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)$$

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

$$\frac{1}{10}x^{2}+\frac{1}{35}x-\frac{3}{4}yx-\frac{3}{14}y+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)$$

Cancel out 2 and 2.

$$\frac{1}{10}x^{2}+\frac{1}{35}x-\frac{3}{4}yx-\frac{3}{14}y-x+2\left(-\frac{1}{7}\right)$$

Combine \frac{1}{35}x and -x to get -\frac{34}{35}x.

$$\frac{1}{10}x^{2}-\frac{34}{35}x-\frac{3}{4}yx-\frac{3}{14}y+2\left(-\frac{1}{7}\right)$$

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

$$\frac{1}{10}x^{2}-\frac{34}{35}x-\frac{3}{4}yx-\frac{3}{14}y+\frac{2\left(-1\right)}{7}$$

Multiply 2 and -1 to get -2.

$$\frac{1}{10}x^{2}-\frac{34}{35}x-\frac{3}{4}yx-\frac{3}{14}y+\frac{-2}{7}$$

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

$$\frac{1}{10}x^{2}-\frac{34}{35}x-\frac{3}{4}yx-\frac{3}{14}y-\frac{2}{7}$$

Expand

$$-\frac{3xy}{4}+\frac{x^{2}}{10}-\frac{3y}{14}-\frac{34x}{35}-\frac{2}{7}$$

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}.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$$\frac{1}{10}x^{2}+\frac{1}{35}x-\frac{3}{4}yx+\frac{-3}{14}y+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)$$

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

$$\frac{1}{10}x^{2}+\frac{1}{35}x-\frac{3}{4}yx-\frac{3}{14}y+2\left(-\frac{1}{2}\right)x+2\left(-\frac{1}{7}\right)$$

Cancel out 2 and 2.

$$\frac{1}{10}x^{2}+\frac{1}{35}x-\frac{3}{4}yx-\frac{3}{14}y-x+2\left(-\frac{1}{7}\right)$$

Combine \frac{1}{35}x and -x to get -\frac{34}{35}x.

$$\frac{1}{10}x^{2}-\frac{34}{35}x-\frac{3}{4}yx-\frac{3}{14}y+2\left(-\frac{1}{7}\right)$$

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

$$\frac{1}{10}x^{2}-\frac{34}{35}x-\frac{3}{4}yx-\frac{3}{14}y+\frac{2\left(-1\right)}{7}$$

Multiply 2 and -1 to get -2.

$$\frac{1}{10}x^{2}-\frac{34}{35}x-\frac{3}{4}yx-\frac{3}{14}y+\frac{-2}{7}$$

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

$$\frac{1}{10}x^{2}-\frac{34}{35}x-\frac{3}{4}yx-\frac{3}{14}y-\frac{2}{7}$$