Solve 25b^2-20b

$$25 b ^ { 2 } - 20 b$$

Factor

$$5b\left(5b-4\right)$$

Solution Steps

Factor out 5.

$$5\left(5b^{2}-4b\right)$$

Consider 5b^{2}-4b. Factor out b.

$$b\left(5b-4\right)$$

Rewrite the complete factored expression.

$$5b\left(5b-4\right)$$

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.

$$25b^{2}-20b=0$$

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.

$$b=\frac{-\left(-20\right)±\sqrt{\left(-20\right)^{2}}}{2\times 25}$$

Take the square root of \left(-20\right)^{2}.

$$b=\frac{-\left(-20\right)±20}{2\times 25}$$

The opposite of -20 is 20.

$$b=\frac{20±20}{2\times 25}$$

Multiply 2 times 25.

$$b=\frac{20±20}{50}$$

Now solve the equation b=\frac{20±20}{50} when ± is plus. Add 20 to 20.

$$b=\frac{40}{50}$$

Reduce the fraction \frac{40}{50} to lowest terms by extracting and canceling out 10.

$$b=\frac{4}{5}$$

Now solve the equation b=\frac{20±20}{50} when ± is minus. Subtract 20 from 20.

$$b=\frac{0}{50}$$

Divide 0 by 50.

$$b=0$$

Factor the original expression using ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right). Substitute \frac{4}{5} for x_{1} and 0 for x_{2}.

$$25b^{2}-20b=25\left(b-\frac{4}{5}\right)b$$

Subtract \frac{4}{5} from b by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$25b^{2}-20b=25\times \frac{5b-4}{5}b$$

Cancel out 5, the greatest common factor in 25 and 5.

$$25b^{2}-20b=5\left(5b-4\right)b$$

Evaluate

$$5b\left(5b-4\right)$$