Solve (4p^2+10/7p-10/7)*(p+5/4)

$$( 4 p ^ { 2 } + \frac { 10 } { 7 p } - \frac { 10 } { 7 } ) \times ( p + \frac { 5 } { 4 } )$$

Evaluate

$$\frac{\left(4p+5\right)\left(14p^{3}-5p+5\right)}{14p}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7p and 7 is 7p. Multiply \frac{10}{7} times \frac{p}{p}.

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

Since \frac{10}{7p} and \frac{10p}{7p} have the same denominator, subtract them by subtracting their numerators.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 4p^{2} times \frac{7p}{7p}.

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

Since \frac{4p^{2}\times 7p}{7p} and \frac{10-10p}{7p} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 4p^{2}\times 7p+10-10p.

$$\frac{28p^{3}+10-10p}{7p}\left(p+\frac{5}{4}\right)$$

Use the distributive property to multiply \frac{28p^{3}+10-10p}{7p} by p+\frac{5}{4}.

$$\frac{28p^{3}+10-10p}{7p}p+\frac{5}{4}\times \frac{28p^{3}+10-10p}{7p}$$

Express \frac{28p^{3}+10-10p}{7p}p as a single fraction.

$$\frac{\left(28p^{3}+10-10p\right)p}{7p}+\frac{5}{4}\times \frac{28p^{3}+10-10p}{7p}$$

Cancel out p in both numerator and denominator.

$$\frac{28p^{3}-10p+10}{7}+\frac{5}{4}\times \frac{28p^{3}+10-10p}{7p}$$

Multiply \frac{5}{4} times \frac{28p^{3}+10-10p}{7p} by multiplying numerator times numerator and denominator times denominator.

$$\frac{28p^{3}-10p+10}{7}+\frac{5\left(28p^{3}+10-10p\right)}{4\times 7p}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7 and 4\times 7p is 4\times 7p. Multiply \frac{28p^{3}-10p+10}{7} times \frac{4p}{4p}.

$$\frac{\left(28p^{3}-10p+10\right)\times 4p}{4\times 7p}+\frac{5\left(28p^{3}+10-10p\right)}{4\times 7p}$$

Since \frac{\left(28p^{3}-10p+10\right)\times 4p}{4\times 7p} and \frac{5\left(28p^{3}+10-10p\right)}{4\times 7p} have the same denominator, add them by adding their numerators.

$$\frac{\left(28p^{3}-10p+10\right)\times 4p+5\left(28p^{3}+10-10p\right)}{4\times 7p}$$

Do the multiplications in \left(28p^{3}-10p+10\right)\times 4p+5\left(28p^{3}+10-10p\right).

$$\frac{112p^{4}-40p^{2}+40p+140p^{3}+50-50p}{4\times 7p}$$

Combine like terms in 112p^{4}-40p^{2}+40p+140p^{3}+50-50p.

$$\frac{112p^{4}-40p^{2}-10p+140p^{3}+50}{4\times 7p}$$

Factor the expressions that are not already factored in \frac{112p^{4}-40p^{2}-10p+140p^{3}+50}{4\times 7p}.

$$\frac{2\left(4p+5\right)\left(14p^{3}-5p+5\right)}{4\times 7p}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\left(4p+5\right)\left(14p^{3}-5p+5\right)}{2\times 7p}$$

Expand 2\times 7p.

$$\frac{\left(4p+5\right)\left(14p^{3}-5p+5\right)}{14p}$$

Use the distributive property to multiply 4p+5 by 14p^{3}-5p+5 and combine like terms.

$$\frac{56p^{4}-20p^{2}-5p+70p^{3}+25}{14p}$$

Expand

$$4p^{3}+5p^{2}-\frac{10p}{7}-\frac{5}{14}+\frac{25}{14p}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7p and 7 is 7p. Multiply \frac{10}{7} times \frac{p}{p}.

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

Since \frac{10}{7p} and \frac{10p}{7p} have the same denominator, subtract them by subtracting their numerators.

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

To add or subtract expressions, expand them to make their denominators the same. Multiply 4p^{2} times \frac{7p}{7p}.

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

Since \frac{4p^{2}\times 7p}{7p} and \frac{10-10p}{7p} have the same denominator, add them by adding their numerators.

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

Do the multiplications in 4p^{2}\times 7p+10-10p.

$$\frac{28p^{3}+10-10p}{7p}\left(p+\frac{5}{4}\right)$$

Use the distributive property to multiply \frac{28p^{3}+10-10p}{7p} by p+\frac{5}{4}.

$$\frac{28p^{3}+10-10p}{7p}p+\frac{5}{4}\times \frac{28p^{3}+10-10p}{7p}$$

Express \frac{28p^{3}+10-10p}{7p}p as a single fraction.

$$\frac{\left(28p^{3}+10-10p\right)p}{7p}+\frac{5}{4}\times \frac{28p^{3}+10-10p}{7p}$$

Cancel out p in both numerator and denominator.

$$\frac{28p^{3}-10p+10}{7}+\frac{5}{4}\times \frac{28p^{3}+10-10p}{7p}$$

Multiply \frac{5}{4} times \frac{28p^{3}+10-10p}{7p} by multiplying numerator times numerator and denominator times denominator.

$$\frac{28p^{3}-10p+10}{7}+\frac{5\left(28p^{3}+10-10p\right)}{4\times 7p}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 7 and 4\times 7p is 4\times 7p. Multiply \frac{28p^{3}-10p+10}{7} times \frac{4p}{4p}.

$$\frac{\left(28p^{3}-10p+10\right)\times 4p}{4\times 7p}+\frac{5\left(28p^{3}+10-10p\right)}{4\times 7p}$$

Since \frac{\left(28p^{3}-10p+10\right)\times 4p}{4\times 7p} and \frac{5\left(28p^{3}+10-10p\right)}{4\times 7p} have the same denominator, add them by adding their numerators.

$$\frac{\left(28p^{3}-10p+10\right)\times 4p+5\left(28p^{3}+10-10p\right)}{4\times 7p}$$

Do the multiplications in \left(28p^{3}-10p+10\right)\times 4p+5\left(28p^{3}+10-10p\right).

$$\frac{112p^{4}-40p^{2}+40p+140p^{3}+50-50p}{4\times 7p}$$

Combine like terms in 112p^{4}-40p^{2}+40p+140p^{3}+50-50p.

$$\frac{112p^{4}-40p^{2}-10p+140p^{3}+50}{4\times 7p}$$

Factor the expressions that are not already factored in \frac{112p^{4}-40p^{2}-10p+140p^{3}+50}{4\times 7p}.

$$\frac{2\left(4p+5\right)\left(14p^{3}-5p+5\right)}{4\times 7p}$$

Cancel out 2 in both numerator and denominator.

$$\frac{\left(4p+5\right)\left(14p^{3}-5p+5\right)}{2\times 7p}$$

Expand 2\times 7p.

$$\frac{\left(4p+5\right)\left(14p^{3}-5p+5\right)}{14p}$$

Use the distributive property to multiply 4p+5 by 14p^{3}-5p+5 and combine like terms.

$$\frac{56p^{4}-20p^{2}-5p+70p^{3}+25}{14p}$$