Solve 56y^2-49y

$$56 { y }^{ 2 } -49y$$

Factor

$$7y\left(8y-7\right)$$

Solution Steps

Factor out 7.

$$7\left(8y^{2}-7y\right)$$

Consider 8y^{2}-7y. Factor out y.

$$y\left(8y-7\right)$$

Rewrite the complete factored expression.

$$7y\left(8y-7\right)$$

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.

$$56y^{2}-49y=0$$

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.

$$y=\frac{-\left(-49\right)±\sqrt{\left(-49\right)^{2}}}{2\times 56}$$

Take the square root of \left(-49\right)^{2}.

$$y=\frac{-\left(-49\right)±49}{2\times 56}$$

The opposite of -49 is 49.

$$y=\frac{49±49}{2\times 56}$$

Multiply 2 times 56.

$$y=\frac{49±49}{112}$$

Now solve the equation y=\frac{49±49}{112} when ± is plus. Add 49 to 49.

$$y=\frac{98}{112}$$

Reduce the fraction \frac{98}{112} to lowest terms by extracting and canceling out 14.

$$y=\frac{7}{8}$$

Now solve the equation y=\frac{49±49}{112} when ± is minus. Subtract 49 from 49.

$$y=\frac{0}{112}$$

Divide 0 by 112.

$$y=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{7}{8} for x_{1} and 0 for x_{2}.

$$56y^{2}-49y=56\left(y-\frac{7}{8}\right)y$$

Subtract \frac{7}{8} from y by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$56y^{2}-49y=56\times \frac{8y-7}{8}y$$

Cancel out 8, the greatest common factor in 56 and 8.

$$56y^{2}-49y=7\left(8y-7\right)y$$

Evaluate

$$7y\left(8y-7\right)$$