Solve 4z^2-8z

$$4 z ^ { 2 } - 8 z$$

Factor

$$4z\left(z-2\right)$$

Solution Steps

Factor out 4.

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

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

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

Rewrite the complete factored expression.

$$4z\left(z-2\right)$$

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.

$$4z^{2}-8z=0$$

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.

$$z=\frac{-\left(-8\right)±\sqrt{\left(-8\right)^{2}}}{2\times 4}$$

Take the square root of \left(-8\right)^{2}.

$$z=\frac{-\left(-8\right)±8}{2\times 4}$$

The opposite of -8 is 8.

$$z=\frac{8±8}{2\times 4}$$

Multiply 2 times 4.

$$z=\frac{8±8}{8}$$

Now solve the equation z=\frac{8±8}{8} when ± is plus. Add 8 to 8.

$$z=\frac{16}{8}$$

Divide 16 by 8.

$$z=2$$

Now solve the equation z=\frac{8±8}{8} when ± is minus. Subtract 8 from 8.

$$z=\frac{0}{8}$$

Divide 0 by 8.

$$z=0$$

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}.

$$4z^{2}-8z=4\left(z-2\right)z$$

Evaluate

$$4z\left(z-2\right)$$