Solve 10b^2-18b

$$10 b ^ { 2 } - 18 b$$

Factor

$$2b\left(5b-9\right)$$

Solution Steps

Factor out 2.

$$2\left(5b^{2}-9b\right)$$

Consider 5b^{2}-9b. Factor out b.

$$b\left(5b-9\right)$$

Rewrite the complete factored expression.

$$2b\left(5b-9\right)$$

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.

$$10b^{2}-18b=0$$

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.

$$b=\frac{-\left(-18\right)±\sqrt{\left(-18\right)^{2}}}{2\times 10}$$

Take the square root of \left(-18\right)^{2}.

$$b=\frac{-\left(-18\right)±18}{2\times 10}$$

The opposite of -18 is 18.

$$b=\frac{18±18}{2\times 10}$$

Multiply 2 times 10.

$$b=\frac{18±18}{20}$$

Now solve the equation b=\frac{18±18}{20} when ± is plus. Add 18 to 18.

$$b=\frac{36}{20}$$

Reduce the fraction \frac{36}{20} to lowest terms by extracting and canceling out 4.

$$b=\frac{9}{5}$$

Now solve the equation b=\frac{18±18}{20} when ± is minus. Subtract 18 from 18.

$$b=\frac{0}{20}$$

Divide 0 by 20.

$$b=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{9}{5} for x_{1} and 0 for x_{2}.

$$10b^{2}-18b=10\left(b-\frac{9}{5}\right)b$$

Subtract \frac{9}{5} from b by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$10b^{2}-18b=10\times \frac{5b-9}{5}b$$

Cancel out 5, the greatest common factor in 10 and 5.

$$10b^{2}-18b=2\left(5b-9\right)b$$

Evaluate

$$2b\left(5b-9\right)$$