Solve 25x^2-2xy+y^2/25

$$25 x ^ { 2 } - 2 x y + \frac { y ^ { 2 } } { 25 }$$

Evaluate

$$\frac{\left(25x-y\right)^{2}}{25}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply 25x^{2}-2xy times \frac{25}{25}.

$$\frac{25\left(25x^{2}-2xy\right)}{25}+\frac{y^{2}}{25}$$

Since \frac{25\left(25x^{2}-2xy\right)}{25} and \frac{y^{2}}{25} have the same denominator, add them by adding their numerators.

$$\frac{25\left(25x^{2}-2xy\right)+y^{2}}{25}$$

Do the multiplications in 25\left(25x^{2}-2xy\right)+y^{2}.

$$\frac{625x^{2}-50xy+y^{2}}{25}$$

Factor

$$\frac{\left(25x-y\right)^{2}}{25}$$

Solution Steps

Factor out \frac{1}{25}.

$$\frac{625x^{2}-50xy+y^{2}}{25}$$

Consider 625x^{2}-50xy+y^{2}. Use the perfect square formula, a^{2}-2ab+b^{2}=\left(a-b\right)^{2}, where a=25x and b=y.

$$\left(25x-y\right)^{2}$$

Rewrite the complete factored expression.

$$\frac{\left(25x-y\right)^{2}}{25}$$