Algebra Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

Multiply by $1$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 1.2.4

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.

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Step 3.1

Multiply $3$ by $1$ .

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

Step 3.2

One to any power is one.

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

Step 3.3

Multiply $3$ by $1$ .

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

Step 3.4

One to any power is one.

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