Solve x-2(x^2-y)/x+2y-4^2

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

Evaluate

$$\frac{-x^{2}+2xy-16x-30y}{x+2y}$$

Short Solution Steps

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

$$\frac{x\left(x+2y\right)}{x+2y}-\frac{2\left(x^{2}-y\right)}{x+2y}-4^{2}$$

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

$$\frac{x\left(x+2y\right)-2\left(x^{2}-y\right)}{x+2y}-4^{2}$$

Do the multiplications in x\left(x+2y\right)-2\left(x^{2}-y\right).

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

Combine like terms in x^{2}+2xy-2x^{2}+2y.

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

Calculate 4 to the power of 2 and get 16.

$$\frac{-x^{2}+2xy+2y}{x+2y}-16$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 16 times \frac{x+2y}{x+2y}.

$$\frac{-x^{2}+2xy+2y}{x+2y}-\frac{16\left(x+2y\right)}{x+2y}$$

Since \frac{-x^{2}+2xy+2y}{x+2y} and \frac{16\left(x+2y\right)}{x+2y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-x^{2}+2xy+2y-16\left(x+2y\right)}{x+2y}$$

Do the multiplications in -x^{2}+2xy+2y-16\left(x+2y\right).

$$\frac{-x^{2}+2xy+2y-16x-32y}{x+2y}$$

Combine like terms in -x^{2}+2xy+2y-16x-32y.

$$\frac{-x^{2}+2xy-30y-16x}{x+2y}$$

Expand

$$\frac{-x^{2}+2xy-16x-30y}{x+2y}$$

Short Solution Steps

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

$$\frac{x\left(x+2y\right)}{x+2y}-\frac{2\left(x^{2}-y\right)}{x+2y}-4^{2}$$

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

$$\frac{x\left(x+2y\right)-2\left(x^{2}-y\right)}{x+2y}-4^{2}$$

Do the multiplications in x\left(x+2y\right)-2\left(x^{2}-y\right).

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

Combine like terms in x^{2}+2xy-2x^{2}+2y.

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

Calculate 4 to the power of 2 and get 16.

$$\frac{-x^{2}+2xy+2y}{x+2y}-16$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 16 times \frac{x+2y}{x+2y}.

$$\frac{-x^{2}+2xy+2y}{x+2y}-\frac{16\left(x+2y\right)}{x+2y}$$

Since \frac{-x^{2}+2xy+2y}{x+2y} and \frac{16\left(x+2y\right)}{x+2y} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-x^{2}+2xy+2y-16\left(x+2y\right)}{x+2y}$$

Do the multiplications in -x^{2}+2xy+2y-16\left(x+2y\right).

$$\frac{-x^{2}+2xy+2y-16x-32y}{x+2y}$$

Combine like terms in -x^{2}+2xy+2y-16x-32y.

$$\frac{-x^{2}+2xy-30y-16x}{x+2y}$$