Solve 2b^2-8/10b^2-25a*50b+250/5b-10

$$\frac { 2 b ^ { 2 } - 8 } { 10 b ^ { 2 } - 25 a } \cdot \frac { 50 b + 250 } { 5 b - 10 }$$

Evaluate

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

Short Solution Steps

Factor the expressions that are not already factored in \frac{50b+250}{5b-10}.

$$\frac{2b^{2}-8}{10b^{2}-25a}\times \frac{50\left(b+5\right)}{5\left(b-2\right)}$$

Cancel out 5 in both numerator and denominator.

$$\frac{2b^{2}-8}{10b^{2}-25a}\times \frac{10\left(b+5\right)}{b-2}$$

Multiply \frac{2b^{2}-8}{10b^{2}-25a} times \frac{10\left(b+5\right)}{b-2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2b^{2}-8\right)\times 10\left(b+5\right)}{\left(10b^{2}-25a\right)\left(b-2\right)}$$

Factor the expressions that are not already factored.

$$\frac{2\times 10\left(b-2\right)\left(b+2\right)\left(b+5\right)}{5\left(b-2\right)\left(-5a+2b^{2}\right)}$$

Cancel out 5\left(b-2\right) in both numerator and denominator.

$$\frac{2\times 2\left(b+2\right)\left(b+5\right)}{-5a+2b^{2}}$$

Expand the expression.

$$\frac{4b^{2}+28b+40}{-5a+2b^{2}}$$

Expand

$$-\frac{4\left(b^{2}+7b+10\right)}{5a-2b^{2}}$$

Short Solution Steps

Factor the expressions that are not already factored in \frac{50b+250}{5b-10}.

$$\frac{2b^{2}-8}{10b^{2}-25a}\times \frac{50\left(b+5\right)}{5\left(b-2\right)}$$

Cancel out 5 in both numerator and denominator.

$$\frac{2b^{2}-8}{10b^{2}-25a}\times \frac{10\left(b+5\right)}{b-2}$$

Multiply \frac{2b^{2}-8}{10b^{2}-25a} times \frac{10\left(b+5\right)}{b-2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(2b^{2}-8\right)\times 10\left(b+5\right)}{\left(10b^{2}-25a\right)\left(b-2\right)}$$

Factor the expressions that are not already factored.

$$\frac{2\times 10\left(b-2\right)\left(b+2\right)\left(b+5\right)}{5\left(b-2\right)\left(-5a+2b^{2}\right)}$$

Cancel out 5\left(b-2\right) in both numerator and denominator.

$$\frac{2\times 2\left(b+2\right)\left(b+5\right)}{-5a+2b^{2}}$$

Expand the expression.

$$\frac{4b^{2}+28b+40}{-5a+2b^{2}}$$