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

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

Evaluate

$$-3xy+\frac{5y^{2}}{4}+x^{2}$$

Solution Steps

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

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

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

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

Combine x\left(-\frac{5}{2}\right)y and -\frac{1}{2}yx to get -3xy.

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

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

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

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

$$x^{2}-3xy+\frac{5}{4}y^{2}$$

Expand

$$-3xy+\frac{5y^{2}}{4}+x^{2}$$

Solution Steps

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

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

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

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

Combine x\left(-\frac{5}{2}\right)y and -\frac{1}{2}yx to get -3xy.

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

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

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

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

$$x^{2}-3xy+\frac{5}{4}y^{2}$$