Solve 4a-a^2

$$4 a - a ^ { 2 }$$

Factor

$$a\left(4-a\right)$$

Solution Steps

Factor out a.

$$a\left(4-a\right)$$

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.

$$-a^{2}+4a=0$$

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.

$$a=\frac{-4±\sqrt{4^{2}}}{2\left(-1\right)}$$

Take the square root of 4^{2}.

$$a=\frac{-4±4}{2\left(-1\right)}$$

Multiply 2 times -1.

$$a=\frac{-4±4}{-2}$$

Now solve the equation a=\frac{-4±4}{-2} when ± is plus. Add -4 to 4.

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

Divide 0 by -2.

$$a=0$$

Now solve the equation a=\frac{-4±4}{-2} when ± is minus. Subtract 4 from -4.

$$a=-\frac{8}{-2}$$

Divide -8 by -2.

$$a=4$$

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 4 for x_{2}.

$$-a^{2}+4a=-a\left(a-4\right)$$

Evaluate

$$a\left(4-a\right)$$