Solve y^2-25y

$$y ^ { 2 } - 25 y$$

Factor

$$y\left(y-25\right)$$

Solution Steps

Factor out y.

$$y\left(y-25\right)$$

Steps Using the Quadratic Formula

Quadratic polynomial can be factored using the transformation ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), where x_{1} and x_{2} are the solutions of the quadratic equation ax^{2}+bx+c=0.

$$y^{2}-25y=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$y=\frac{-\left(-25\right)±\sqrt{\left(-25\right)^{2}}}{2}$$

Take the square root of \left(-25\right)^{2}.

$$y=\frac{-\left(-25\right)±25}{2}$$

The opposite of -25 is 25.

$$y=\frac{25±25}{2}$$

Now solve the equation y=\frac{25±25}{2} when ± is plus. Add 25 to 25.

$$y=\frac{50}{2}$$

Divide 50 by 2.

$$y=25$$

Now solve the equation y=\frac{25±25}{2} when ± is minus. Subtract 25 from 25.

$$y=\frac{0}{2}$$

Divide 0 by 2.

$$y=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 25 for x_{1} and 0 for x_{2}.

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

Evaluate

$$y\left(y-25\right)$$