Solve 5y^2-10y

$$5 y ^ { 2 } - 10 y$$

Factor

$$5y\left(y-2\right)$$

Solution Steps

Factor out 5.

$$5\left(y^{2}-2y\right)$$

Consider y^{2}-2y. Factor out y.

$$y\left(y-2\right)$$

Rewrite the complete factored expression.

$$5y\left(y-2\right)$$

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.

$$5y^{2}-10y=0$$

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.

$$y=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}}}{2\times 5}$$

Take the square root of \left(-10\right)^{2}.

$$y=\frac{-\left(-10\right)±10}{2\times 5}$$

The opposite of -10 is 10.

$$y=\frac{10±10}{2\times 5}$$

Multiply 2 times 5.

$$y=\frac{10±10}{10}$$

Now solve the equation y=\frac{10±10}{10} when ± is plus. Add 10 to 10.

$$y=\frac{20}{10}$$

Divide 20 by 10.

$$y=2$$

Now solve the equation y=\frac{10±10}{10} when ± is minus. Subtract 10 from 10.

$$y=\frac{0}{10}$$

Divide 0 by 10.

$$y=0$$

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

$$5y^{2}-10y=5\left(y-2\right)y$$

Evaluate

$$5y\left(y-2\right)$$