Solve 25y^2-10y

$$25 { y }^{ 2 } -10y$$

Factor

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

Solution Steps

Factor out 5.

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

Consider 5y^{2}-2y. Factor out y.

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

Rewrite the complete factored expression.

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

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.

$$25y^{2}-10y=0$$

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.

$$y=\frac{-\left(-10\right)±\sqrt{\left(-10\right)^{2}}}{2\times 25}$$

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

$$y=\frac{-\left(-10\right)±10}{2\times 25}$$

The opposite of -10 is 10.

$$y=\frac{10±10}{2\times 25}$$

Multiply 2 times 25.

$$y=\frac{10±10}{50}$$

Now solve the equation y=\frac{10±10}{50} when ± is plus. Add 10 to 10.

$$y=\frac{20}{50}$$

Reduce the fraction \frac{20}{50} to lowest terms by extracting and canceling out 10.

$$y=\frac{2}{5}$$

Now solve the equation y=\frac{10±10}{50} when ± is minus. Subtract 10 from 10.

$$y=\frac{0}{50}$$

Divide 0 by 50.

$$y=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{2}{5} for x_{1} and 0 for x_{2}.

$$25y^{2}-10y=25\left(y-\frac{2}{5}\right)y$$

Subtract \frac{2}{5} from y by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$25y^{2}-10y=25\times \frac{5y-2}{5}y$$

Cancel out 5, the greatest common factor in 25 and 5.

$$25y^{2}-10y=5\left(5y-2\right)y$$

Evaluate

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