Solve (x+1/2)*(2y-1.5x)

$$(x+ \frac{ 1 }{ 2 } ) \times (2y-1.5x)$$

Evaluate

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

Solution Steps

Apply the distributive property by multiplying each term of x+\frac{1}{2} by each term of 2y-1.5x.

$$2xy-1.5x^{2}+\frac{1}{2}\times 2y+\frac{1}{2}\left(-1.5\right)x$$

Cancel out 2 and 2.

$$2xy-1.5x^{2}+y+\frac{1}{2}\left(-1.5\right)x$$

Convert decimal number -1.5 to fraction -\frac{15}{10}. Reduce the fraction -\frac{15}{10} to lowest terms by extracting and canceling out 5.

$$2xy-1.5x^{2}+y+\frac{1}{2}\left(-\frac{3}{2}\right)x$$

Multiply \frac{1}{2} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$2xy-1.5x^{2}+y+\frac{1\left(-3\right)}{2\times 2}x$$

Do the multiplications in the fraction \frac{1\left(-3\right)}{2\times 2}.

$$2xy-1.5x^{2}+y+\frac{-3}{4}x$$

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$2xy-1.5x^{2}+y-\frac{3}{4}x$$

Expand

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

Solution Steps

Apply the distributive property by multiplying each term of x+\frac{1}{2} by each term of 2y-1.5x.

$$2xy-1.5x^{2}+\frac{1}{2}\times 2y+\frac{1}{2}\left(-1.5\right)x$$

Cancel out 2 and 2.

$$2xy-1.5x^{2}+y+\frac{1}{2}\left(-1.5\right)x$$

Convert decimal number -1.5 to fraction -\frac{15}{10}. Reduce the fraction -\frac{15}{10} to lowest terms by extracting and canceling out 5.

$$2xy-1.5x^{2}+y+\frac{1}{2}\left(-\frac{3}{2}\right)x$$

Multiply \frac{1}{2} times -\frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$2xy-1.5x^{2}+y+\frac{1\left(-3\right)}{2\times 2}x$$

Do the multiplications in the fraction \frac{1\left(-3\right)}{2\times 2}.

$$2xy-1.5x^{2}+y+\frac{-3}{4}x$$

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$2xy-1.5x^{2}+y-\frac{3}{4}x$$