Simplify 4n(3n^2+n-4)-n(3-n)

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

Step 1

Simplify each term.

Apply the distributive property.

$4 n (3 n^{2}) + 4 n \cdot n + 4 n \cdot - 4 - n (3 - n)$

Simplify.

Rewrite using the commutative property of multiplication.

$4 \cdot 3 n \cdot n^{2} + 4 n \cdot n + 4 n \cdot - 4 - n (3 - n)$

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

Move $n$ .

$4 \cdot 3 n \cdot n^{2} + 4 (n \cdot n) + 4 n \cdot - 4 - n (3 - n)$

Multiply $n$ by $n$ .

$4 \cdot 3 n \cdot n^{2} + 4 n^{2} + 4 n \cdot - 4 - n (3 - n)$

Multiply $- 4$ by $4$ .

$4 \cdot 3 n \cdot n^{2} + 4 n^{2} - 16 n - n (3 - n)$

Simplify each term.

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

Move $n^{2}$ .

$4 \cdot 3 (n^{2} n) + 4 n^{2} - 16 n - n (3 - n)$

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

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

$4 \cdot 3 (n^{2} n^{1}) + 4 n^{2} - 16 n - n (3 - n)$

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

$4 \cdot 3 n^{2 + 1} + 4 n^{2} - 16 n - n (3 - n)$

Add $2$ and $1$ .

$4 \cdot 3 n^{3} + 4 n^{2} - 16 n - n (3 - n)$

Multiply $4$ by $3$ .

$12 n^{3} + 4 n^{2} - 16 n - n (3 - n)$

Apply the distributive property.

$12 n^{3} + 4 n^{2} - 16 n - n \cdot 3 - n (- n)$

Multiply $3$ by $- 1$ .

$12 n^{3} + 4 n^{2} - 16 n - 3 n - n (- n)$

Rewrite using the commutative property of multiplication.

$12 n^{3} + 4 n^{2} - 16 n - 3 n - 1 \cdot - 1 n \cdot n$

Simplify each term.

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

Move $n$ .

$12 n^{3} + 4 n^{2} - 16 n - 3 n - 1 \cdot - 1 (n \cdot n)$

Multiply $n$ by $n$ .

$12 n^{3} + 4 n^{2} - 16 n - 3 n - 1 \cdot - 1 n^{2}$

Multiply $- 1$ by $- 1$ .

$12 n^{3} + 4 n^{2} - 16 n - 3 n + 1 n^{2}$

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

$12 n^{3} + 4 n^{2} - 16 n - 3 n + n^{2}$

Step 2

Simplify by adding terms.

Add $4 n^{2}$ and $n^{2}$ .

$12 n^{3} + 5 n^{2} - 16 n - 3 n$

Subtract $3 n$ from $- 16 n$ .

$12 n^{3} + 5 n^{2} - 19 n$

Simplify 4n(3n^2+n-4)-n(3-n)

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