Simplify ((a+b)^3)/18*2/((a+b)^2)

$\frac{{(a + b)}^{3}}{18} \cdot \frac{2}{{(a + b)}^{2}}$

Step 1

Combine.

$\frac{{(a + b)}^{3} \cdot 2}{18 {(a + b)}^{2}}$

Step 2

Cancel the common factor of ${(a + b)}^{3}$ and ${(a + b)}^{2}$ .

Factor ${(a + b)}^{2}$ out of ${(a + b)}^{3} \cdot 2$ .

$\frac{{(a + b)}^{2} ((a + b) \cdot 2)}{18 {(a + b)}^{2}}$

Cancel the common factors.

Factor ${(a + b)}^{2}$ out of $18 {(a + b)}^{2}$ .

$\frac{{(a + b)}^{2} ((a + b) \cdot 2)}{{(a + b)}^{2} \cdot 18}$

Cancel the common factor.

$\frac{{(a + b)}^{2} ((a + b) \cdot 2)}{{(a + b)}^{2} \cdot 18}$

Rewrite the expression.

$\frac{(a + b) \cdot 2}{18}$

Step 3

Cancel the common factor of $2$ and $18$ .

Factor $2$ out of $(a + b) \cdot 2$ .

$\frac{2 \cdot (a + b)}{18}$

Cancel the common factors.

Factor $2$ out of $18$ .

$\frac{2 \cdot (a + b)}{2 \cdot 9}$

Cancel the common factor.

$\frac{2 \cdot (a + b)}{2 \cdot 9}$

Rewrite the expression.

$\frac{a + b}{9}$