Solve p+q/2p^2*8p^3/p^2-2p+1

$$\frac { p + q } { 2 p ^ { 2 } } \cdot \frac { 8 p ^ { 3 } } { p ^ { 2 } - 2 p + 1 }$$

Evaluate

$$\frac{4p\left(p+q\right)}{\left(p-1\right)^{2}}$$

Short Solution Steps

Multiply \frac{p+q}{2p^{2}} times \frac{8p^{3}}{p^{2}-2p+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(p+q\right)\times 8p^{3}}{2p^{2}\left(p^{2}-2p+1\right)}$$

Cancel out 2p^{2} in both numerator and denominator.

$$\frac{4p\left(p+q\right)}{p^{2}-2p+1}$$

Use the distributive property to multiply 4p by p+q.

$$\frac{4p^{2}+4pq}{p^{2}-2p+1}$$

Expand

$$\frac{4\left(p^{2}+pq\right)}{p^{2}-2p+1}$$

Short Solution Steps

Multiply \frac{p+q}{2p^{2}} times \frac{8p^{3}}{p^{2}-2p+1} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(p+q\right)\times 8p^{3}}{2p^{2}\left(p^{2}-2p+1\right)}$$

Cancel out 2p^{2} in both numerator and denominator.

$$\frac{4p\left(p+q\right)}{p^{2}-2p+1}$$

Use the distributive property to multiply 4p by p+q.

$$\frac{4p^{2}+4pq}{p^{2}-2p+1}$$