Simplify ((y+1)^5)/((y+1)^2)

$\frac{{(y + 1)}^{5}}{{(y + 1)}^{2}}$

Step 1

Cancel the common factor of ${(y + 1)}^{5}$ and ${(y + 1)}^{2}$ .

Factor ${(y + 1)}^{2}$ out of ${(y + 1)}^{5}$ .

$\frac{{(y + 1)}^{2} {(y + 1)}^{3}}{{(y + 1)}^{2}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{{(y + 1)}^{2} {(y + 1)}^{3}}{{(y + 1)}^{2} \cdot 1}$

Cancel the common factor.

$\frac{{(y + 1)}^{2} {(y + 1)}^{3}}{{(y + 1)}^{2} \cdot 1}$

Rewrite the expression.

$\frac{{(y + 1)}^{3}}{1}$

Divide ${(y + 1)}^{3}$ by $1$ .

${(y + 1)}^{3}$

Step 2

Use the Binomial Theorem.

$y^{3} + 3 y^{2} \cdot 1 + 3 y \cdot 1^{2} + 1^{3}$

Step 3

Simplify each term.

Multiply $3$ by $1$ .

$y^{3} + 3 y^{2} + 3 y \cdot 1^{2} + 1^{3}$

One to any power is one.

$y^{3} + 3 y^{2} + 3 y \cdot 1 + 1^{3}$

Multiply $3$ by $1$ .

$y^{3} + 3 y^{2} + 3 y + 1^{3}$

One to any power is one.

$y^{3} + 3 y^{2} + 3 y + 1$