Algebra Examples

$P {(1 + \frac{r}{2})}^{2}$

Step 1

Rewrite ${(1 + \frac{r}{2})}^{2}$ as $(1 + \frac{r}{2}) (1 + \frac{r}{2})$ .

$P ((1 + \frac{r}{2}) (1 + \frac{r}{2}))$

Step 2

Expand $(1 + \frac{r}{2}) (1 + \frac{r}{2})$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$P (1 (1 + \frac{r}{2}) + \frac{r}{2} (1 + \frac{r}{2}))$

Step 2.2

Apply the distributive property.

$P (1 \cdot 1 + 1 \frac{r}{2} + \frac{r}{2} (1 + \frac{r}{2}))$

Step 2.3

Apply the distributive property.

$P (1 \cdot 1 + 1 \frac{r}{2} + \frac{r}{2} \cdot 1 + \frac{r}{2} \cdot \frac{r}{2})$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $1$ by $1$ .

$P (1 + 1 \frac{r}{2} + \frac{r}{2} \cdot 1 + \frac{r}{2} \cdot \frac{r}{2})$

Step 3.1.2

Multiply $\frac{r}{2}$ by $1$ .

$P (1 + \frac{r}{2} + \frac{r}{2} \cdot 1 + \frac{r}{2} \cdot \frac{r}{2})$

Step 3.1.3

Multiply $\frac{r}{2}$ by $1$ .

$P (1 + \frac{r}{2} + \frac{r}{2} + \frac{r}{2} \cdot \frac{r}{2})$

Step 3.1.4

Multiply $\frac{r}{2} \cdot \frac{r}{2}$ .

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Step 3.1.4.1

Multiply $\frac{r}{2}$ by $\frac{r}{2}$ .

$P (1 + \frac{r}{2} + \frac{r}{2} + \frac{r \cdot r}{2 \cdot 2})$

Step 3.1.4.2

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

$P (1 + \frac{r}{2} + \frac{r}{2} + \frac{r^{1} r}{2 \cdot 2})$

Step 3.1.4.3

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

$P (1 + \frac{r}{2} + \frac{r}{2} + \frac{r^{1} r^{1}}{2 \cdot 2})$

Step 3.1.4.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$P (1 + \frac{r}{2} + \frac{r}{2} + \frac{r^{1 + 1}}{2 \cdot 2})$

Step 3.1.4.5

Add $1$ and $1$ .

$P (1 + \frac{r}{2} + \frac{r}{2} + \frac{r^{2}}{2 \cdot 2})$

Step 3.1.4.6

Multiply $2$ by $2$ .

$P (1 + \frac{r}{2} + \frac{r}{2} + \frac{r^{2}}{4})$

Step 3.2

Add $\frac{r}{2}$ and $\frac{r}{2}$ .

$P (1 + 2 \frac{r}{2} + \frac{r^{2}}{4})$

Step 4

Cancel the common factor of $2$ .

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Step 4.1

Cancel the common factor.

$P (1 + 2 \frac{r}{2} + \frac{r^{2}}{4})$

Step 4.2

Rewrite the expression.

$P (1 + r + \frac{r^{2}}{4})$

Step 5

Apply the distributive property.

$P \cdot 1 + P r + P \frac{r^{2}}{4}$

Step 6

Simplify.

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Step 6.1

Multiply $P$ by $1$ .

$P + P r + P \frac{r^{2}}{4}$

Step 6.2

Combine $P$ and $\frac{r^{2}}{4}$ .

$P + P r + \frac{P r^{2}}{4}$

Step 7

Reorder $P$ and $r$ .

$P + r P + \frac{P r^{2}}{4}$

Step 8

Reorder $P$ and $r^{2}$ .

$P + r P + \frac{r^{2} P}{4}$

Step 9

Move $P$ .

$r P + \frac{r^{2} P}{4} + P$

Step 10

Reorder $r P$ and $\frac{r^{2} P}{4}$ .

$\frac{r^{2} P}{4} + r P + P$