Solve 16a^2-4a

$$16 a ^ { 2 } - 4 a$$

Factor

$$4a\left(4a-1\right)$$

Solution Steps

Factor out 4.

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

Consider 4a^{2}-a. Factor out a.

$$a\left(4a-1\right)$$

Rewrite the complete factored expression.

$$4a\left(4a-1\right)$$

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.

$$16a^{2}-4a=0$$

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.

$$a=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}}}{2\times 16}$$

Take the square root of \left(-4\right)^{2}.

$$a=\frac{-\left(-4\right)±4}{2\times 16}$$

The opposite of -4 is 4.

$$a=\frac{4±4}{2\times 16}$$

Multiply 2 times 16.

$$a=\frac{4±4}{32}$$

Now solve the equation a=\frac{4±4}{32} when ± is plus. Add 4 to 4.

$$a=\frac{8}{32}$$

Reduce the fraction \frac{8}{32} to lowest terms by extracting and canceling out 8.

$$a=\frac{1}{4}$$

Now solve the equation a=\frac{4±4}{32} when ± is minus. Subtract 4 from 4.

$$a=\frac{0}{32}$$

Divide 0 by 32.

$$a=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{1}{4} for x_{1} and 0 for x_{2}.

$$16a^{2}-4a=16\left(a-\frac{1}{4}\right)a$$

Subtract \frac{1}{4} from a by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$16a^{2}-4a=16\times \frac{4a-1}{4}a$$

Cancel out 4, the greatest common factor in 16 and 4.

$$16a^{2}-4a=4\left(4a-1\right)a$$

Evaluate

$$4a\left(4a-1\right)$$