Solve 8r^2+56r

$$8 r ^ { 2 } + 56 r$$

Factor

$$8r\left(r+7\right)$$

Solution Steps

Factor out 8.

$$8\left(r^{2}+7r\right)$$

Consider r^{2}+7r. Factor out r.

$$r\left(r+7\right)$$

Rewrite the complete factored expression.

$$8r\left(r+7\right)$$

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.

$$8r^{2}+56r=0$$

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.

$$r=\frac{-56±\sqrt{56^{2}}}{2\times 8}$$

Take the square root of 56^{2}.

$$r=\frac{-56±56}{2\times 8}$$

Multiply 2 times 8.

$$r=\frac{-56±56}{16}$$

Now solve the equation r=\frac{-56±56}{16} when ± is plus. Add -56 to 56.

$$r=\frac{0}{16}$$

Divide 0 by 16.

$$r=0$$

Now solve the equation r=\frac{-56±56}{16} when ± is minus. Subtract 56 from -56.

$$r=-\frac{112}{16}$$

Divide -112 by 16.

$$r=-7$$

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 -7 for x_{2}.

$$8r^{2}+56r=8r\left(r-\left(-7\right)\right)$$

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

$$8r^{2}+56r=8r\left(r+7\right)$$

Evaluate

$$8r\left(r+7\right)$$