Write in Standard Form (1-2n)^3-7n(n^2-2)

${(1 - 2 n)}^{3} - 7 n (n^{2} - 2)$

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Simplify each term.

Use the Binomial Theorem.

$1^{3} + 3 \cdot 1^{2} (- 2 n) + 3 \cdot 1 {(- 2 n)}^{2} + {(- 2 n)}^{3} - 7 n (n^{2} - 2)$

Simplify each term.

One to any power is one.

$1 + 3 \cdot 1^{2} (- 2 n) + 3 \cdot 1 {(- 2 n)}^{2} + {(- 2 n)}^{3} - 7 n (n^{2} - 2)$

One to any power is one.

$1 + 3 \cdot 1 (- 2 n) + 3 \cdot 1 {(- 2 n)}^{2} + {(- 2 n)}^{3} - 7 n (n^{2} - 2)$

Multiply $3$ by $1$ .

$1 + 3 (- 2 n) + 3 \cdot 1 {(- 2 n)}^{2} + {(- 2 n)}^{3} - 7 n (n^{2} - 2)$

Multiply $- 2$ by $3$ .

$1 - 6 n + 3 \cdot 1 {(- 2 n)}^{2} + {(- 2 n)}^{3} - 7 n (n^{2} - 2)$

Multiply $3$ by $1$ .

$1 - 6 n + 3 {(- 2 n)}^{2} + {(- 2 n)}^{3} - 7 n (n^{2} - 2)$

Apply the product rule to $- 2 n$ .

$1 - 6 n + 3 ({(- 2)}^{2} n^{2}) + {(- 2 n)}^{3} - 7 n (n^{2} - 2)$

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

$1 - 6 n + 3 (4 n^{2}) + {(- 2 n)}^{3} - 7 n (n^{2} - 2)$

Multiply $4$ by $3$ .

$1 - 6 n + 12 n^{2} + {(- 2 n)}^{3} - 7 n (n^{2} - 2)$

Apply the product rule to $- 2 n$ .

$1 - 6 n + 12 n^{2} + {(- 2)}^{3} n^{3} - 7 n (n^{2} - 2)$

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

$1 - 6 n + 12 n^{2} - 8 n^{3} - 7 n (n^{2} - 2)$

Simplify the expression.

Move $1$ .

$- 6 n + 12 n^{2} - 8 n^{3} + 1 - 7 n (n^{2} - 2)$

Move $- 6 n$ .

$12 n^{2} - 8 n^{3} - 6 n + 1 - 7 n (n^{2} - 2)$

Reorder $12 n^{2}$ and $- 8 n^{3}$ .

$- 8 n^{3} + 12 n^{2} - 6 n + 1 - 7 n (n^{2} - 2)$