Simplify ((a+b)^9)/((a+b)^4)

$\frac{{(a + b)}^{9}}{{(a + b)}^{4}}$

Step 1

Cancel the common factor of ${(a + b)}^{9}$ and ${(a + b)}^{4}$ .

Factor ${(a + b)}^{4}$ out of ${(a + b)}^{9}$ .

$\frac{{(a + b)}^{4} {(a + b)}^{5}}{{(a + b)}^{4}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{{(a + b)}^{4} {(a + b)}^{5}}{{(a + b)}^{4} \cdot 1}$

Cancel the common factor.

$\frac{{(a + b)}^{4} {(a + b)}^{5}}{{(a + b)}^{4} \cdot 1}$

Rewrite the expression.

$\frac{{(a + b)}^{5}}{1}$

Divide ${(a + b)}^{5}$ by $1$ .

${(a + b)}^{5}$

Step 2

Use the Binomial Theorem.

$a^{5} + 5 a^{4} b + 10 a^{3} b^{2} + 10 a^{2} b^{3} + 5 a b^{4} + b^{5}$