Finite Math Examples

$1^{3} + 2^{3} + 3^{3} + \frac{n^{2} {(n + 1)}^{2}}{4}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

One to any power is one.

$1 + 2^{3} + 3^{3} + \frac{n^{2} {(n + 1)}^{2}}{4}$

Step 1.2

Raise $2$ to the power of $3$ .

$1 + 8 + 3^{3} + \frac{n^{2} {(n + 1)}^{2}}{4}$

Step 1.3

Raise $3$ to the power of $3$ .

$1 + 8 + 27 + \frac{n^{2} {(n + 1)}^{2}}{4}$

Step 2

Simplify by adding numbers.

Tap for more steps...

Step 2.1

Add $1$ and $8$ .

$9 + 27 + \frac{n^{2} {(n + 1)}^{2}}{4}$

Step 2.2

Add $9$ and $27$ .

$36 + \frac{n^{2} {(n + 1)}^{2}}{4}$

Step 3

To write $36$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$36 \cdot \frac{4}{4} + \frac{n^{2} {(n + 1)}^{2}}{4}$

Step 4

Simplify terms.

Tap for more steps...

Step 4.1

Combine $36$ and $\frac{4}{4}$ .

$\frac{36 \cdot 4}{4} + \frac{n^{2} {(n + 1)}^{2}}{4}$

Step 4.2

Combine the numerators over the common denominator.

$\frac{36 \cdot 4 + n^{2} {(n + 1)}^{2}}{4}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Multiply $36$ by $4$ .

$\frac{144 + n^{2} {(n + 1)}^{2}}{4}$

Step 5.2

Rewrite ${(n + 1)}^{2}$ as $(n + 1) (n + 1)$ .

$\frac{144 + n^{2} ((n + 1) (n + 1))}{4}$

Step 5.3

Expand $(n + 1) (n + 1)$ using the FOIL Method.

Tap for more steps...

Step 5.3.1

Apply the distributive property.

$\frac{144 + n^{2} (n (n + 1) + 1 (n + 1))}{4}$

Step 5.3.2

Apply the distributive property.

$\frac{144 + n^{2} (n \cdot n + n \cdot 1 + 1 (n + 1))}{4}$

Step 5.3.3

Apply the distributive property.

$\frac{144 + n^{2} (n \cdot n + n \cdot 1 + 1 n + 1 \cdot 1)}{4}$

Step 5.4

Simplify and combine like terms.

Tap for more steps...

Step 5.4.1

Simplify each term.

Tap for more steps...

Step 5.4.1.1

Multiply $n$ by $n$ .

$\frac{144 + n^{2} (n^{2} + n \cdot 1 + 1 n + 1 \cdot 1)}{4}$

Step 5.4.1.2

Multiply $n$ by $1$ .

$\frac{144 + n^{2} (n^{2} + n + 1 n + 1 \cdot 1)}{4}$

Step 5.4.1.3

Multiply $n$ by $1$ .

$\frac{144 + n^{2} (n^{2} + n + n + 1 \cdot 1)}{4}$

Step 5.4.1.4

Multiply $1$ by $1$ .

$\frac{144 + n^{2} (n^{2} + n + n + 1)}{4}$

Step 5.4.2

Add $n$ and $n$ .

$\frac{144 + n^{2} (n^{2} + 2 n + 1)}{4}$

Step 5.5

Apply the distributive property.

$\frac{144 + n^{2} n^{2} + n^{2} (2 n) + n^{2} \cdot 1}{4}$

Step 5.6

Simplify.

Tap for more steps...

Step 5.6.1

Multiply $n^{2}$ by $n^{2}$ by adding the exponents.

Tap for more steps...

Step 5.6.1.1

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

$\frac{144 + n^{2 + 2} + n^{2} (2 n) + n^{2} \cdot 1}{4}$

Step 5.6.1.2

Add $2$ and $2$ .

$\frac{144 + n^{4} + n^{2} (2 n) + n^{2} \cdot 1}{4}$

Step 5.6.2

Rewrite using the commutative property of multiplication.

$\frac{144 + n^{4} + 2 n^{2} n + n^{2} \cdot 1}{4}$

Step 5.6.3

Multiply $n^{2}$ by $1$ .

$\frac{144 + n^{4} + 2 n^{2} n + n^{2}}{4}$

Step 5.7

Multiply $n^{2}$ by $n$ by adding the exponents.

Tap for more steps...

Step 5.7.1

Move $n$ .

$\frac{144 + n^{4} + 2 (n \cdot n^{2}) + n^{2}}{4}$

Step 5.7.2

Multiply $n$ by $n^{2}$ .

Tap for more steps...

Step 5.7.2.1

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

$\frac{144 + n^{4} + 2 (n^{1} n^{2}) + n^{2}}{4}$

Step 5.7.2.2

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

$\frac{144 + n^{4} + 2 n^{1 + 2} + n^{2}}{4}$

Step 5.7.3

Add $1$ and $2$ .

$\frac{144 + n^{4} + 2 n^{3} + n^{2}}{4}$

Step 5.8

Reorder terms.

$\frac{n^{4} + 2 n^{3} + n^{2} + 144}{4}$