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

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

Evaluate

$$\frac{12x^{2}}{5}-\frac{15y^{2}}{4}$$

Solution Steps

Use the distributive property to multiply 3 by 2x-\frac{5}{2}y.

$$\left(6x+3\left(-\frac{5}{2}\right)y\right)\left(\frac{2}{5}x+\frac{1}{2}y\right)$$

Express 3\left(-\frac{5}{2}\right) as a single fraction.

$$\left(6x+\frac{3\left(-5\right)}{2}y\right)\left(\frac{2}{5}x+\frac{1}{2}y\right)$$

Multiply 3 and -5 to get -15.

$$\left(6x+\frac{-15}{2}y\right)\left(\frac{2}{5}x+\frac{1}{2}y\right)$$

Fraction \frac{-15}{2} can be rewritten as -\frac{15}{2} by extracting the negative sign.

$$\left(6x-\frac{15}{2}y\right)\left(\frac{2}{5}x+\frac{1}{2}y\right)$$

Apply the distributive property by multiplying each term of 6x-\frac{15}{2}y by each term of \frac{2}{5}x+\frac{1}{2}y.

$$6x\times \frac{2}{5}x+6x\times \frac{1}{2}y-\frac{15}{2}y\times \frac{2}{5}x-\frac{15}{2}y\times \frac{1}{2}y$$

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

$$6x^{2}\times \frac{2}{5}+6x\times \frac{1}{2}y-\frac{15}{2}y\times \frac{2}{5}x-\frac{15}{2}y\times \frac{1}{2}y$$

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

$$6x^{2}\times \frac{2}{5}+6x\times \frac{1}{2}y-\frac{15}{2}y\times \frac{2}{5}x-\frac{15}{2}y^{2}\times \frac{1}{2}$$

Express 6\times \frac{2}{5} as a single fraction.

$$\frac{6\times 2}{5}x^{2}+6x\times \frac{1}{2}y-\frac{15}{2}y\times \frac{2}{5}x-\frac{15}{2}y^{2}\times \frac{1}{2}$$

Multiply 6 and 2 to get 12.

$$\frac{12}{5}x^{2}+6x\times \frac{1}{2}y-\frac{15}{2}y\times \frac{2}{5}x-\frac{15}{2}y^{2}\times \frac{1}{2}$$

Multiply 6 and \frac{1}{2} to get \frac{6}{2}.

$$\frac{12}{5}x^{2}+\frac{6}{2}xy-\frac{15}{2}y\times \frac{2}{5}x-\frac{15}{2}y^{2}\times \frac{1}{2}$$

Divide 6 by 2 to get 3.

$$\frac{12}{5}x^{2}+3xy-\frac{15}{2}y\times \frac{2}{5}x-\frac{15}{2}y^{2}\times \frac{1}{2}$$

Multiply -\frac{15}{2} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12}{5}x^{2}+3xy+\frac{-15\times 2}{2\times 5}yx-\frac{15}{2}y^{2}\times \frac{1}{2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{12}{5}x^{2}+3xy+\frac{-15}{5}yx-\frac{15}{2}y^{2}\times \frac{1}{2}$$

Divide -15 by 5 to get -3.

$$\frac{12}{5}x^{2}+3xy-3yx-\frac{15}{2}y^{2}\times \frac{1}{2}$$

Combine 3xy and -3yx to get 0.

$$\frac{12}{5}x^{2}-\frac{15}{2}y^{2}\times \frac{1}{2}$$

Multiply -\frac{15}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12}{5}x^{2}+\frac{-15}{2\times 2}y^{2}$$

Do the multiplications in the fraction \frac{-15}{2\times 2}.

$$\frac{12}{5}x^{2}+\frac{-15}{4}y^{2}$$

Fraction \frac{-15}{4} can be rewritten as -\frac{15}{4} by extracting the negative sign.

$$\frac{12}{5}x^{2}-\frac{15}{4}y^{2}$$

Expand

$$\frac{12x^{2}}{5}-\frac{15y^{2}}{4}$$

Solution Steps

Use the distributive property to multiply 3 by 2x-\frac{5}{2}y.

$$\left(6x+3\left(-\frac{5}{2}\right)y\right)\left(\frac{2}{5}x+\frac{1}{2}y\right)$$

Express 3\left(-\frac{5}{2}\right) as a single fraction.

$$\left(6x+\frac{3\left(-5\right)}{2}y\right)\left(\frac{2}{5}x+\frac{1}{2}y\right)$$

Multiply 3 and -5 to get -15.

$$\left(6x+\frac{-15}{2}y\right)\left(\frac{2}{5}x+\frac{1}{2}y\right)$$

Fraction \frac{-15}{2} can be rewritten as -\frac{15}{2} by extracting the negative sign.

$$\left(6x-\frac{15}{2}y\right)\left(\frac{2}{5}x+\frac{1}{2}y\right)$$

Apply the distributive property by multiplying each term of 6x-\frac{15}{2}y by each term of \frac{2}{5}x+\frac{1}{2}y.

$$6x\times \frac{2}{5}x+6x\times \frac{1}{2}y-\frac{15}{2}y\times \frac{2}{5}x-\frac{15}{2}y\times \frac{1}{2}y$$

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

$$6x^{2}\times \frac{2}{5}+6x\times \frac{1}{2}y-\frac{15}{2}y\times \frac{2}{5}x-\frac{15}{2}y\times \frac{1}{2}y$$

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

$$6x^{2}\times \frac{2}{5}+6x\times \frac{1}{2}y-\frac{15}{2}y\times \frac{2}{5}x-\frac{15}{2}y^{2}\times \frac{1}{2}$$

Express 6\times \frac{2}{5} as a single fraction.

$$\frac{6\times 2}{5}x^{2}+6x\times \frac{1}{2}y-\frac{15}{2}y\times \frac{2}{5}x-\frac{15}{2}y^{2}\times \frac{1}{2}$$

Multiply 6 and 2 to get 12.

$$\frac{12}{5}x^{2}+6x\times \frac{1}{2}y-\frac{15}{2}y\times \frac{2}{5}x-\frac{15}{2}y^{2}\times \frac{1}{2}$$

Multiply 6 and \frac{1}{2} to get \frac{6}{2}.

$$\frac{12}{5}x^{2}+\frac{6}{2}xy-\frac{15}{2}y\times \frac{2}{5}x-\frac{15}{2}y^{2}\times \frac{1}{2}$$

Divide 6 by 2 to get 3.

$$\frac{12}{5}x^{2}+3xy-\frac{15}{2}y\times \frac{2}{5}x-\frac{15}{2}y^{2}\times \frac{1}{2}$$

Multiply -\frac{15}{2} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12}{5}x^{2}+3xy+\frac{-15\times 2}{2\times 5}yx-\frac{15}{2}y^{2}\times \frac{1}{2}$$

Cancel out 2 in both numerator and denominator.

$$\frac{12}{5}x^{2}+3xy+\frac{-15}{5}yx-\frac{15}{2}y^{2}\times \frac{1}{2}$$

Divide -15 by 5 to get -3.

$$\frac{12}{5}x^{2}+3xy-3yx-\frac{15}{2}y^{2}\times \frac{1}{2}$$

Combine 3xy and -3yx to get 0.

$$\frac{12}{5}x^{2}-\frac{15}{2}y^{2}\times \frac{1}{2}$$

Multiply -\frac{15}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{12}{5}x^{2}+\frac{-15}{2\times 2}y^{2}$$

Do the multiplications in the fraction \frac{-15}{2\times 2}.

$$\frac{12}{5}x^{2}+\frac{-15}{4}y^{2}$$

Fraction \frac{-15}{4} can be rewritten as -\frac{15}{4} by extracting the negative sign.

$$\frac{12}{5}x^{2}-\frac{15}{4}y^{2}$$