Solve m^2+2m

$$m ^ { 2 } + 2 m$$

Factor

$$m\left(m+2\right)$$

Solution Steps

Factor out m.

$$m\left(m+2\right)$$

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.

$$m^{2}+2m=0$$

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.

$$m=\frac{-2±\sqrt{2^{2}}}{2}$$

Take the square root of 2^{2}.

$$m=\frac{-2±2}{2}$$

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

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

Divide 0 by 2.

$$m=0$$

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

$$m=-\frac{4}{2}$$

Divide -4 by 2.

$$m=-2$$

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

$$m^{2}+2m=m\left(m-\left(-2\right)\right)$$

Simplify all the expressions of the form p-\left(-q\right) to p+q.

$$m^{2}+2m=m\left(m+2\right)$$

Evaluate

$$m\left(m+2\right)$$