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

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

Evaluate

$$-\frac{y^{2}}{4}+9x^{2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x times \frac{2}{2}.

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

Since \frac{2\times 3x}{2} and \frac{y}{2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2\times 3x+y.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x times \frac{2}{2}.

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

Since -\frac{y}{2} and \frac{2\times 3x}{2} have the same denominator, add them by adding their numerators.

$$\frac{6x+y}{2}\times \frac{-y+2\times 3x}{2}$$

Do the multiplications in -y+2\times 3x.

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

Multiply \frac{6x+y}{2} times \frac{-y+6x}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(6x+y\right)\left(-y+6x\right)}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{\left(6x+y\right)\left(-y+6x\right)}{4}$$

Apply the distributive property by multiplying each term of 6x+y by each term of -y+6x.

$$\frac{-6xy+36x^{2}-y^{2}+6yx}{4}$$

Combine -6xy and 6yx to get 0.

$$\frac{36x^{2}-y^{2}}{4}$$

Expand

$$-\frac{y^{2}}{4}+9x^{2}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x times \frac{2}{2}.

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

Since \frac{2\times 3x}{2} and \frac{y}{2} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 2\times 3x+y.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 3x times \frac{2}{2}.

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

Since -\frac{y}{2} and \frac{2\times 3x}{2} have the same denominator, add them by adding their numerators.

$$\frac{6x+y}{2}\times \frac{-y+2\times 3x}{2}$$

Do the multiplications in -y+2\times 3x.

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

Multiply \frac{6x+y}{2} times \frac{-y+6x}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(6x+y\right)\left(-y+6x\right)}{2\times 2}$$

Multiply 2 and 2 to get 4.

$$\frac{\left(6x+y\right)\left(-y+6x\right)}{4}$$

Apply the distributive property by multiplying each term of 6x+y by each term of -y+6x.

$$\frac{-6xy+36x^{2}-y^{2}+6yx}{4}$$

Combine -6xy and 6yx to get 0.

$$\frac{36x^{2}-y^{2}}{4}$$