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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

Express 2\times \frac{2}{5} as a single fraction.

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

Multiply 2 and 2 to get 4.

$$\frac{4}{5}x^{2}+2x\times \frac{1}{2}y-\frac{5}{2}y\times \frac{2}{5}x-\frac{5}{2}y^{2}\times \frac{1}{2}$$

Cancel out 2 and 2.

$$\frac{4}{5}x^{2}+xy-\frac{5}{2}y\times \frac{2}{5}x-\frac{5}{2}y^{2}\times \frac{1}{2}$$

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

$$\frac{4}{5}x^{2}+xy+\frac{-5\times 2}{2\times 5}yx-\frac{5}{2}y^{2}\times \frac{1}{2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{4}{5}x^{2}+xy+\frac{-5}{5}yx-\frac{5}{2}y^{2}\times \frac{1}{2}$$

Divide -5 by 5 to get -1.

$$\frac{4}{5}x^{2}+xy-yx-\frac{5}{2}y^{2}\times \frac{1}{2}$$

Combine xy and -yx to get 0.

$$\frac{4}{5}x^{2}-\frac{5}{2}y^{2}\times \frac{1}{2}$$

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

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

Do the multiplications in the fraction \frac{-5}{2\times 2}.

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

Fraction \frac{-5}{4} can be rewritten as -\frac{5}{4} by extracting the negative sign.

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

Expand

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

Solution Steps

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

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

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

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

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

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

Express 2\times \frac{2}{5} as a single fraction.

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

Multiply 2 and 2 to get 4.

$$\frac{4}{5}x^{2}+2x\times \frac{1}{2}y-\frac{5}{2}y\times \frac{2}{5}x-\frac{5}{2}y^{2}\times \frac{1}{2}$$

Cancel out 2 and 2.

$$\frac{4}{5}x^{2}+xy-\frac{5}{2}y\times \frac{2}{5}x-\frac{5}{2}y^{2}\times \frac{1}{2}$$

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

$$\frac{4}{5}x^{2}+xy+\frac{-5\times 2}{2\times 5}yx-\frac{5}{2}y^{2}\times \frac{1}{2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{4}{5}x^{2}+xy+\frac{-5}{5}yx-\frac{5}{2}y^{2}\times \frac{1}{2}$$

Divide -5 by 5 to get -1.

$$\frac{4}{5}x^{2}+xy-yx-\frac{5}{2}y^{2}\times \frac{1}{2}$$

Combine xy and -yx to get 0.

$$\frac{4}{5}x^{2}-\frac{5}{2}y^{2}\times \frac{1}{2}$$

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

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

Do the multiplications in the fraction \frac{-5}{2\times 2}.

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

Fraction \frac{-5}{4} can be rewritten as -\frac{5}{4} by extracting the negative sign.

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