Finite Math Examples

$(n^{4} + n^{3} \log (n)) (\log (n) + 5) + (3 \log (n + 7)) (n^{4} + 20)$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Expand $(n^{4} + n^{3} \log (n)) (\log (n) + 5)$ using the FOIL Method.

Tap for more steps...

Step 1.1.1

Apply the distributive property.

$n^{4} (\log (n) + 5) + n^{3} \log (n) (\log (n) + 5) + (3 \log (n + 7)) (n^{4} + 20)$

Step 1.1.2

Apply the distributive property.

$n^{4} \log (n) + n^{4} \cdot 5 + n^{3} \log (n) (\log (n) + 5) + (3 \log (n + 7)) (n^{4} + 20)$

Step 1.1.3

Apply the distributive property.

$n^{4} \log (n) + n^{4} \cdot 5 + n^{3} \log (n) \log (n) + n^{3} \log (n) \cdot 5 + (3 \log (n + 7)) (n^{4} + 20)$

Step 1.2

Simplify each term.

Tap for more steps...

Step 1.2.1

Move $5$ to the left of $n^{4}$ .

$n^{4} \log (n) + 5 \cdot n^{4} + n^{3} \log (n) \log (n) + n^{3} \log (n) \cdot 5 + (3 \log (n + 7)) (n^{4} + 20)$

Step 1.2.2

Multiply $n^{3} \log (n) \log (n)$ .

Tap for more steps...

Step 1.2.2.1

Raise $\log (n)$ to the power of $1$ .

$n^{4} \log (n) + 5 n^{4} + n^{3} (\log^{1} (n) \log (n)) + n^{3} \log (n) \cdot 5 + (3 \log (n + 7)) (n^{4} + 20)$

Step 1.2.2.2

Raise $\log (n)$ to the power of $1$ .

$n^{4} \log (n) + 5 n^{4} + n^{3} (\log^{1} (n) \log^{1} (n)) + n^{3} \log (n) \cdot 5 + (3 \log (n + 7)) (n^{4} + 20)$

Step 1.2.2.3

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

$n^{4} \log (n) + 5 n^{4} + n^{3} {\log (n)}^{1 + 1} + n^{3} \log (n) \cdot 5 + (3 \log (n + 7)) (n^{4} + 20)$

Step 1.2.2.4

Add $1$ and $1$ .

$n^{4} \log (n) + 5 n^{4} + n^{3} \log^{2} (n) + n^{3} \log (n) \cdot 5 + (3 \log (n + 7)) (n^{4} + 20)$

Step 1.2.3

Move $5$ to the left of $n^{3} \log (n)$ .

$n^{4} \log (n) + 5 n^{4} + n^{3} \log^{2} (n) + 5 n^{3} \log (n) + (3 \log (n + 7)) (n^{4} + 20)$

Step 1.3

Apply the distributive property.

$n^{4} \log (n) + 5 n^{4} + n^{3} \log^{2} (n) + 5 n^{3} \log (n) + 3 \log (n + 7) n^{4} + 3 \log (n + 7) \cdot 20$

Step 1.4

Multiply $20$ by $3$ .

$n^{4} \log (n) + 5 n^{4} + n^{3} \log^{2} (n) + 5 n^{3} \log (n) + 3 \log (n + 7) n^{4} + 60 \log (n + 7)$

Step 2

Reorder factors in $n^{4} \log (n) + 5 n^{4} + n^{3} \log^{2} (n) + 5 n^{3} \log (n) + 3 \log (n + 7) n^{4} + 60 \log (n + 7)$ .

$n^{4} \log (n) + 5 n^{4} + n^{3} \log^{2} (n) + 5 n^{3} \log (n) + 3 n^{4} \log (n + 7) + 60 \log (n + 7)$