Solve 5xy-7x^2-y^2div4y-x

$$5 x y - 7 x ^ { 2 } - y ^ { 2 } \div 4 y - x$$

Evaluate

$$-\frac{y^{3}}{4}+5xy-7x^{2}-x$$

Short Solution Steps

Express \frac{y^{2}}{4}y as a single fraction.

$$5xy-7x^{2}-\frac{y^{2}y}{4}-x$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$5xy-7x^{2}-\frac{y^{3}}{4}-x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 5xy-7x^{2} times \frac{4}{4}.

$$\frac{4\left(5xy-7x^{2}\right)}{4}-\frac{y^{3}}{4}-x$$

Since \frac{4\left(5xy-7x^{2}\right)}{4} and \frac{y^{3}}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4\left(5xy-7x^{2}\right)-y^{3}}{4}-x$$

Do the multiplications in 4\left(5xy-7x^{2}\right)-y^{3}.

$$\frac{20xy-28x^{2}-y^{3}}{4}-x$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x times \frac{4}{4}.

$$\frac{20xy-28x^{2}-y^{3}}{4}-\frac{4x}{4}$$

Since \frac{20xy-28x^{2}-y^{3}}{4} and \frac{4x}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20xy-28x^{2}-y^{3}-4x}{4}$$

Factor

$$\frac{-28x^{2}+20xy-4x-y^{3}}{4}$$

Solution Steps

Factor out \frac{1}{4}.

$$\frac{20xy-28x^{2}-y^{2}y-4x}{4}$$