Simplify 3n^2(5n^2-2n+1)+(4n^2-11n^4-9)

$3 n^{2} (5 n^{2} - 2 n + 1) + (4 n^{2} - 11 n^{4} - 9)$

Remove parentheses.

$3 n^{2} (5 n^{2} - 2 n + 1) + 4 n^{2} - 11 n^{4} - 9$

Simplify each term.

Apply the distributive property.

$3 n^{2} (5 n^{2}) + 3 n^{2} (- 2 n) + 3 n^{2} \cdot 1 + 4 n^{2} - 11 n^{4} - 9$

Simplify.

Rewrite using the commutative property of multiplication.

$3 \cdot 5 n^{2} n^{2} + 3 n^{2} (- 2 n) + 3 n^{2} \cdot 1 + 4 n^{2} - 11 n^{4} - 9$

Rewrite using the commutative property of multiplication.

$3 \cdot 5 n^{2} n^{2} + 3 \cdot - 2 n^{2} n + 3 n^{2} \cdot 1 + 4 n^{2} - 11 n^{4} - 9$

Multiply $3$ by $1$ .

$3 \cdot 5 n^{2} n^{2} + 3 \cdot - 2 n^{2} n + 3 n^{2} + 4 n^{2} - 11 n^{4} - 9$

Simplify each term.

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

Move $n^{2}$ .

$3 \cdot 5 (n^{2} n^{2}) + 3 \cdot - 2 n^{2} n + 3 n^{2} + 4 n^{2} - 11 n^{4} - 9$

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

$3 \cdot 5 n^{2 + 2} + 3 \cdot - 2 n^{2} n + 3 n^{2} + 4 n^{2} - 11 n^{4} - 9$

Add $2$ and $2$ .

$3 \cdot 5 n^{4} + 3 \cdot - 2 n^{2} n + 3 n^{2} + 4 n^{2} - 11 n^{4} - 9$

Multiply $3$ by $5$ .

$15 n^{4} + 3 \cdot - 2 n^{2} n + 3 n^{2} + 4 n^{2} - 11 n^{4} - 9$

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

Move $n$ .

$15 n^{4} + 3 \cdot - 2 (n \cdot n^{2}) + 3 n^{2} + 4 n^{2} - 11 n^{4} - 9$

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

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

$15 n^{4} + 3 \cdot - 2 (n^{1} n^{2}) + 3 n^{2} + 4 n^{2} - 11 n^{4} - 9$

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

$15 n^{4} + 3 \cdot - 2 n^{1 + 2} + 3 n^{2} + 4 n^{2} - 11 n^{4} - 9$

Add $1$ and $2$ .

$15 n^{4} + 3 \cdot - 2 n^{3} + 3 n^{2} + 4 n^{2} - 11 n^{4} - 9$

Multiply $3$ by $- 2$ .

$15 n^{4} - 6 n^{3} + 3 n^{2} + 4 n^{2} - 11 n^{4} - 9$

Simplify by adding terms.

Subtract $11 n^{4}$ from $15 n^{4}$ .

$4 n^{4} - 6 n^{3} + 3 n^{2} + 4 n^{2} - 9$

Add $3 n^{2}$ and $4 n^{2}$ .

$4 n^{4} - 6 n^{3} + 7 n^{2} - 9$