Solve 7y^2-14y

$$7 y ^ { 2 } - 14 y$$

Factor

$$7y\left(y-2\right)$$

Solution Steps

Factor out 7.

$$7\left(y^{2}-2y\right)$$

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

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

Rewrite the complete factored expression.

$$7y\left(y-2\right)$$

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.

$$7y^{2}-14y=0$$

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.

$$y=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}}}{2\times 7}$$

Take the square root of \left(-14\right)^{2}.

$$y=\frac{-\left(-14\right)±14}{2\times 7}$$

The opposite of -14 is 14.

$$y=\frac{14±14}{2\times 7}$$

Multiply 2 times 7.

$$y=\frac{14±14}{14}$$

Now solve the equation y=\frac{14±14}{14} when ± is plus. Add 14 to 14.

$$y=\frac{28}{14}$$

Divide 28 by 14.

$$y=2$$

Now solve the equation y=\frac{14±14}{14} when ± is minus. Subtract 14 from 14.

$$y=\frac{0}{14}$$

Divide 0 by 14.

$$y=0$$

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}.

$$7y^{2}-14y=7\left(y-2\right)y$$

Evaluate

$$7y\left(y-2\right)$$