Solve (1/2x-y)(-2x-5y)

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

Divide -2 by 2 to get -1.

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

Multiply \frac{1}{2} and -5 to get \frac{-5}{2}.

$$-x^{2}+\frac{-5}{2}xy+2yx+5y^{2}$$

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$-x^{2}-\frac{5}{2}xy+2yx+5y^{2}$$

Combine -\frac{5}{2}xy and 2yx to get -\frac{1}{2}xy.

$$-x^{2}-\frac{1}{2}xy+5y^{2}$$

Expand

$$-\frac{xy}{2}+5y^{2}-x^{2}$$

Solution Steps

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

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

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

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

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

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

Divide -2 by 2 to get -1.

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

Multiply \frac{1}{2} and -5 to get \frac{-5}{2}.

$$-x^{2}+\frac{-5}{2}xy+2yx+5y^{2}$$

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$-x^{2}-\frac{5}{2}xy+2yx+5y^{2}$$

Combine -\frac{5}{2}xy and 2yx to get -\frac{1}{2}xy.

$$-x^{2}-\frac{1}{2}xy+5y^{2}$$