Solve 4u^2+8u

$$4 u ^ { 2 } + 8 u$$

Factor

$$4u\left(u+2\right)$$

Solution Steps

Factor out 4.

$$4\left(u^{2}+2u\right)$$

Consider u^{2}+2u. Factor out u.

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

Rewrite the complete factored expression.

$$4u\left(u+2\right)$$

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.

$$4u^{2}+8u=0$$

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.

$$u=\frac{-8±\sqrt{8^{2}}}{2\times 4}$$

Take the square root of 8^{2}.

$$u=\frac{-8±8}{2\times 4}$$

Multiply 2 times 4.

$$u=\frac{-8±8}{8}$$

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

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

Divide 0 by 8.

$$u=0$$

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

$$u=-\frac{16}{8}$$

Divide -16 by 8.

$$u=-2$$

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}.

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

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

$$4u^{2}+8u=4u\left(u+2\right)$$

Evaluate

$$4u\left(u+2\right)$$