Solve (-1/4x-y)(--2/4x+y)

$$( - \frac { 1 } { 4 } x - y ) ( - \frac { - 2 } { 4 } x + y )$$

Evaluate

$$-\frac{\left(x+2y\right)\left(x+4y\right)}{8}$$

Solution Steps

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

$$\left(-\frac{1}{4}x-y\right)\left(\left(-\left(-\frac{1}{2}\right)\right)x+y\right)$$

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$\left(-\frac{1}{4}x-y\right)\left(\frac{1}{2}x+y\right)$$

Apply the distributive property by multiplying each term of -\frac{1}{4}x-y by each term of \frac{1}{2}x+y.

$$-\frac{1}{4}x\times \frac{1}{2}x-\frac{1}{4}xy-y\times \frac{1}{2}x-y^{2}$$

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

$$-\frac{1}{4}x^{2}\times \frac{1}{2}-\frac{1}{4}xy-y\times \frac{1}{2}x-y^{2}$$

Multiply -\frac{1}{4} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-1}{4\times 2}x^{2}-\frac{1}{4}xy-y\times \frac{1}{2}x-y^{2}$$

Do the multiplications in the fraction \frac{-1}{4\times 2}.

$$\frac{-1}{8}x^{2}-\frac{1}{4}xy-y\times \frac{1}{2}x-y^{2}$$

Fraction \frac{-1}{8} can be rewritten as -\frac{1}{8} by extracting the negative sign.

$$-\frac{1}{8}x^{2}-\frac{1}{4}xy-y\times \frac{1}{2}x-y^{2}$$

Multiply -1 and \frac{1}{2} to get -\frac{1}{2}.

$$-\frac{1}{8}x^{2}-\frac{1}{4}xy-\frac{1}{2}yx-y^{2}$$

Combine -\frac{1}{4}xy and -\frac{1}{2}yx to get -\frac{3}{4}xy.

$$-\frac{1}{8}x^{2}-\frac{3}{4}xy-y^{2}$$

Expand

$$-\frac{3xy}{4}-\frac{x^{2}}{8}-y^{2}$$

Solution Steps

Reduce the fraction \frac{-2}{4} to lowest terms by extracting and canceling out 2.

$$\left(-\frac{1}{4}x-y\right)\left(\left(-\left(-\frac{1}{2}\right)\right)x+y\right)$$

The opposite of -\frac{1}{2} is \frac{1}{2}.

$$\left(-\frac{1}{4}x-y\right)\left(\frac{1}{2}x+y\right)$$

Apply the distributive property by multiplying each term of -\frac{1}{4}x-y by each term of \frac{1}{2}x+y.

$$-\frac{1}{4}x\times \frac{1}{2}x-\frac{1}{4}xy-y\times \frac{1}{2}x-y^{2}$$

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

$$-\frac{1}{4}x^{2}\times \frac{1}{2}-\frac{1}{4}xy-y\times \frac{1}{2}x-y^{2}$$

Multiply -\frac{1}{4} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-1}{4\times 2}x^{2}-\frac{1}{4}xy-y\times \frac{1}{2}x-y^{2}$$

Do the multiplications in the fraction \frac{-1}{4\times 2}.

$$\frac{-1}{8}x^{2}-\frac{1}{4}xy-y\times \frac{1}{2}x-y^{2}$$

Fraction \frac{-1}{8} can be rewritten as -\frac{1}{8} by extracting the negative sign.

$$-\frac{1}{8}x^{2}-\frac{1}{4}xy-y\times \frac{1}{2}x-y^{2}$$

Multiply -1 and \frac{1}{2} to get -\frac{1}{2}.

$$-\frac{1}{8}x^{2}-\frac{1}{4}xy-\frac{1}{2}yx-y^{2}$$

Combine -\frac{1}{4}xy and -\frac{1}{2}yx to get -\frac{3}{4}xy.

$$-\frac{1}{8}x^{2}-\frac{3}{4}xy-y^{2}$$