Solve 16y^2-81y

$$16 y ^ { 2 } - 81 y$$

Factor

$$y\left(16y-81\right)$$

Solution Steps

Factor out y.

$$y\left(16y-81\right)$$

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.

$$16y^{2}-81y=0$$

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.

$$y=\frac{-\left(-81\right)±\sqrt{\left(-81\right)^{2}}}{2\times 16}$$

Take the square root of \left(-81\right)^{2}.

$$y=\frac{-\left(-81\right)±81}{2\times 16}$$

The opposite of -81 is 81.

$$y=\frac{81±81}{2\times 16}$$

Multiply 2 times 16.

$$y=\frac{81±81}{32}$$

Now solve the equation y=\frac{81±81}{32} when ± is plus. Add 81 to 81.

$$y=\frac{162}{32}$$

Reduce the fraction \frac{162}{32} to lowest terms by extracting and canceling out 2.

$$y=\frac{81}{16}$$

Now solve the equation y=\frac{81±81}{32} when ± is minus. Subtract 81 from 81.

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

Divide 0 by 32.

$$y=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{81}{16} for x_{1} and 0 for x_{2}.

$$16y^{2}-81y=16\left(y-\frac{81}{16}\right)y$$

Subtract \frac{81}{16} from y by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$16y^{2}-81y=16\times \frac{16y-81}{16}y$$

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

$$16y^{2}-81y=\left(16y-81\right)y$$

Evaluate

$$y\left(16y-81\right)$$