Divide (40p^3+2p^2+40p)÷8p^2

$(40 p^{3} + 2 p^{2} + 40 p) \div 8 p^{2}$

Step 1

Rewrite the division as a fraction.

$\frac{40 p^{3} + 2 p^{2} + 40 p}{8 p^{2}}$

Step 2

Factor $2 p$ out of $40 p^{3} + 2 p^{2} + 40 p$ .

Factor $2 p$ out of $40 p^{3}$ .

$\frac{2 p (20 p^{2}) + 2 p^{2} + 40 p}{8 p^{2}}$

Factor $2 p$ out of $2 p^{2}$ .

$\frac{2 p (20 p^{2}) + 2 p (p) + 40 p}{8 p^{2}}$

Factor $2 p$ out of $40 p$ .

$\frac{2 p (20 p^{2}) + 2 p (p) + 2 p (20)}{8 p^{2}}$

Factor $2 p$ out of $2 p (20 p^{2}) + 2 p (p)$ .

$\frac{2 p (20 p^{2} + p) + 2 p (20)}{8 p^{2}}$

Factor $2 p$ out of $2 p (20 p^{2} + p) + 2 p (20)$ .

$\frac{2 p (20 p^{2} + p + 20)}{8 p^{2}}$

Step 3

Cancel the common factor of $2$ and $8$ .

Factor $2$ out of $2 p (20 p^{2} + p + 20)$ .

$\frac{2 (p (20 p^{2} + p + 20))}{8 p^{2}}$

Cancel the common factors.

Factor $2$ out of $8 p^{2}$ .

$\frac{2 (p (20 p^{2} + p + 20))}{2 (4 p^{2})}$

Cancel the common factor.

$\frac{2 (p (20 p^{2} + p + 20))}{2 (4 p^{2})}$

Rewrite the expression.

$\frac{p (20 p^{2} + p + 20)}{4 p^{2}}$

Step 4

Cancel the common factors.

Factor $p$ out of $4 p^{2}$ .

$\frac{p (20 p^{2} + p + 20)}{p (4 p)}$

Cancel the common factor.

$\frac{p (20 p^{2} + p + 20)}{p (4 p)}$

Rewrite the expression.

$\frac{20 p^{2} + p + 20}{4 p}$

Step 5

Split the fraction $\frac{20 p^{2} + p + 20}{4 p}$ into two fractions.

$\frac{20 p^{2} + p}{4 p} + \frac{20}{4 p}$

Step 6

Split the fraction $\frac{20 p^{2} + p}{4 p}$ into two fractions.

$\frac{20 p^{2}}{4 p} + \frac{p}{4 p} + \frac{20}{4 p}$

Step 7

Cancel the common factor of $20$ and $4$ .

Factor $4$ out of $20 p^{2}$ .

$\frac{4 (5 p^{2})}{4 p} + \frac{p}{4 p} + \frac{20}{4 p}$

Cancel the common factors.

Factor $4$ out of $4 p$ .

$\frac{4 (5 p^{2})}{4 (p)} + \frac{p}{4 p} + \frac{20}{4 p}$

Cancel the common factor.

$\frac{4 (5 p^{2})}{4 p} + \frac{p}{4 p} + \frac{20}{4 p}$

Rewrite the expression.

$\frac{5 p^{2}}{p} + \frac{p}{4 p} + \frac{20}{4 p}$

Step 8

Cancel the common factor of $p^{2}$ and $p$ .

Factor $p$ out of $5 p^{2}$ .

$\frac{p (5 p)}{p} + \frac{p}{4 p} + \frac{20}{4 p}$

Cancel the common factors.

Raise $p$ to the power of $1$ .

$\frac{p (5 p)}{p^{1}} + \frac{p}{4 p} + \frac{20}{4 p}$

Factor $p$ out of $p^{1}$ .

$\frac{p (5 p)}{p \cdot 1} + \frac{p}{4 p} + \frac{20}{4 p}$

Cancel the common factor.

$\frac{p (5 p)}{p \cdot 1} + \frac{p}{4 p} + \frac{20}{4 p}$

Rewrite the expression.

$\frac{5 p}{1} + \frac{p}{4 p} + \frac{20}{4 p}$

Divide $5 p$ by $1$ .

$5 p + \frac{p}{4 p} + \frac{20}{4 p}$

Step 9

Cancel the common factor of $p$ .

Cancel the common factor.

$5 p + \frac{p}{4 p} + \frac{20}{4 p}$

Rewrite the expression.

$5 p + \frac{1}{4} + \frac{20}{4 p}$

Step 10

Cancel the common factor of $20$ and $4$ .

Factor $4$ out of $20$ .

$5 p + \frac{1}{4} + \frac{4 \cdot 5}{4 p}$

Cancel the common factors.

Factor $4$ out of $4 p$ .

$5 p + \frac{1}{4} + \frac{4 \cdot 5}{4 (p)}$

Cancel the common factor.

$5 p + \frac{1}{4} + \frac{4 \cdot 5}{4 p}$

Rewrite the expression.

$5 p + \frac{1}{4} + \frac{5}{p}$

Divide (40p^3+2p^2+40p)÷8p^2

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