Calculus Examples

$a = 1$ , $b = 1$ , $u (n) u (n - 2) + u (n - 1)$

Step 1

Replace the variable $a$ with $1$ in the expression.

$u (n) \cdot (u (n - 2)) + u (n - 1)$

Step 2

Simplify each term.

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Step 2.1

Multiply $u$ by $u$ by adding the exponents.

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Step 2.1.1

Move $u$ .

$u \cdot u n \cdot (n - 2) + u (n - 1)$

Step 2.1.2

Multiply $u$ by $u$ .

$u^{2} n \cdot (n - 2) + u (n - 1)$

Step 2.2

Apply the distributive property.

$u^{2} n \cdot n + u^{2} n \cdot - 2 + u (n - 1)$

Step 2.3

Multiply $n$ by $n$ by adding the exponents.

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Step 2.3.1

Move $n$ .

$u^{2} (n \cdot n) + u^{2} n \cdot - 2 + u (n - 1)$

Step 2.3.2

Multiply $n$ by $n$ .

$u^{2} n^{2} + u^{2} n \cdot - 2 + u (n - 1)$

Step 2.4

Move $- 2$ to the left of $u^{2} n$ .

$u^{2} n^{2} - 2 \cdot (u^{2} n) + u (n - 1)$

Step 2.5

Remove parentheses.

$u^{2} n^{2} - 2 u^{2} n + u (n - 1)$

Step 2.6

Apply the distributive property.

$u^{2} n^{2} - 2 u^{2} n + u n + u \cdot - 1$

Step 2.7

Move $- 1$ to the left of $u$ .

$u^{2} n^{2} - 2 u^{2} n + u n - 1 \cdot u$

Step 2.8

Rewrite $- 1 u$ as $- u$ .

$u^{2} n^{2} - 2 u^{2} n + u n - u$