Solve a^2-9a

$$a ^ { 2 } - 9 a$$

Factor

$$a\left(a-9\right)$$

Solution Steps

Factor out a.

$$a\left(a-9\right)$$

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.

$$a^{2}-9a=0$$

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.

$$a=\frac{-\left(-9\right)±\sqrt{\left(-9\right)^{2}}}{2}$$

Take the square root of \left(-9\right)^{2}.

$$a=\frac{-\left(-9\right)±9}{2}$$

The opposite of -9 is 9.

$$a=\frac{9±9}{2}$$

Now solve the equation a=\frac{9±9}{2} when ± is plus. Add 9 to 9.

$$a=\frac{18}{2}$$

Divide 18 by 2.

$$a=9$$

Now solve the equation a=\frac{9±9}{2} when ± is minus. Subtract 9 from 9.

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

Divide 0 by 2.

$$a=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute 9 for x_{1} and 0 for x_{2}.

$$a^{2}-9a=\left(a-9\right)a$$

Evaluate

$$a\left(a-9\right)$$