Simplify (x^3+3x^2+1)(3x^2+6x-2)

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

Expand $(x^{3} + 3 x^{2} + 1) (3 x^{2} + 6 x - 2)$ by multiplying each term in the first expression by each term in the second expression.

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

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

Multiply $x^{3}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

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

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

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

Add $2$ and $3$ .

$3 x^{5} + x^{3} (6 x) + x^{3} \cdot - 2 + 3 x^{2} (3 x^{2}) + 3 x^{2} (6 x) + 3 x^{2} \cdot - 2 + 1 (3 x^{2}) + 1 (6 x) + 1 \cdot - 2$

Rewrite using the commutative property of multiplication.

$3 x^{5} + 6 x^{3} x + x^{3} \cdot - 2 + 3 x^{2} (3 x^{2}) + 3 x^{2} (6 x) + 3 x^{2} \cdot - 2 + 1 (3 x^{2}) + 1 (6 x) + 1 \cdot - 2$

Multiply $x^{3}$ by $x$ by adding the exponents.

Move $x$ .

$3 x^{5} + 6 (x \cdot x^{3}) + x^{3} \cdot - 2 + 3 x^{2} (3 x^{2}) + 3 x^{2} (6 x) + 3 x^{2} \cdot - 2 + 1 (3 x^{2}) + 1 (6 x) + 1 \cdot - 2$

Multiply $x$ by $x^{3}$ .

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

$3 x^{5} + 6 (x^{1} x^{3}) + x^{3} \cdot - 2 + 3 x^{2} (3 x^{2}) + 3 x^{2} (6 x) + 3 x^{2} \cdot - 2 + 1 (3 x^{2}) + 1 (6 x) + 1 \cdot - 2$

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

$3 x^{5} + 6 x^{1 + 3} + x^{3} \cdot - 2 + 3 x^{2} (3 x^{2}) + 3 x^{2} (6 x) + 3 x^{2} \cdot - 2 + 1 (3 x^{2}) + 1 (6 x) + 1 \cdot - 2$

Add $1$ and $3$ .

$3 x^{5} + 6 x^{4} + x^{3} \cdot - 2 + 3 x^{2} (3 x^{2}) + 3 x^{2} (6 x) + 3 x^{2} \cdot - 2 + 1 (3 x^{2}) + 1 (6 x) + 1 \cdot - 2$

Move $- 2$ to the left of $x^{3}$ .

$3 x^{5} + 6 x^{4} - 2 \cdot x^{3} + 3 x^{2} (3 x^{2}) + 3 x^{2} (6 x) + 3 x^{2} \cdot - 2 + 1 (3 x^{2}) + 1 (6 x) + 1 \cdot - 2$

Rewrite using the commutative property of multiplication.

$3 x^{5} + 6 x^{4} - 2 x^{3} + 3 \cdot 3 x^{2} x^{2} + 3 x^{2} (6 x) + 3 x^{2} \cdot - 2 + 1 (3 x^{2}) + 1 (6 x) + 1 \cdot - 2$

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

Move $x^{2}$ .

$3 x^{5} + 6 x^{4} - 2 x^{3} + 3 \cdot 3 (x^{2} x^{2}) + 3 x^{2} (6 x) + 3 x^{2} \cdot - 2 + 1 (3 x^{2}) + 1 (6 x) + 1 \cdot - 2$

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

$3 x^{5} + 6 x^{4} - 2 x^{3} + 3 \cdot 3 x^{2 + 2} + 3 x^{2} (6 x) + 3 x^{2} \cdot - 2 + 1 (3 x^{2}) + 1 (6 x) + 1 \cdot - 2$

Add $2$ and $2$ .

$3 x^{5} + 6 x^{4} - 2 x^{3} + 3 \cdot 3 x^{4} + 3 x^{2} (6 x) + 3 x^{2} \cdot - 2 + 1 (3 x^{2}) + 1 (6 x) + 1 \cdot - 2$

Multiply $3$ by $3$ .

$3 x^{5} + 6 x^{4} - 2 x^{3} + 9 x^{4} + 3 x^{2} (6 x) + 3 x^{2} \cdot - 2 + 1 (3 x^{2}) + 1 (6 x) + 1 \cdot - 2$

Rewrite using the commutative property of multiplication.

$3 x^{5} + 6 x^{4} - 2 x^{3} + 9 x^{4} + 3 \cdot 6 x^{2} x + 3 x^{2} \cdot - 2 + 1 (3 x^{2}) + 1 (6 x) + 1 \cdot - 2$

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

Move $x$ .

$3 x^{5} + 6 x^{4} - 2 x^{3} + 9 x^{4} + 3 \cdot 6 (x \cdot x^{2}) + 3 x^{2} \cdot - 2 + 1 (3 x^{2}) + 1 (6 x) + 1 \cdot - 2$

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

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

$3 x^{5} + 6 x^{4} - 2 x^{3} + 9 x^{4} + 3 \cdot 6 (x^{1} x^{2}) + 3 x^{2} \cdot - 2 + 1 (3 x^{2}) + 1 (6 x) + 1 \cdot - 2$

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

$3 x^{5} + 6 x^{4} - 2 x^{3} + 9 x^{4} + 3 \cdot 6 x^{1 + 2} + 3 x^{2} \cdot - 2 + 1 (3 x^{2}) + 1 (6 x) + 1 \cdot - 2$

Add $1$ and $2$ .

$3 x^{5} + 6 x^{4} - 2 x^{3} + 9 x^{4} + 3 \cdot 6 x^{3} + 3 x^{2} \cdot - 2 + 1 (3 x^{2}) + 1 (6 x) + 1 \cdot - 2$

Multiply $3$ by $6$ .

$3 x^{5} + 6 x^{4} - 2 x^{3} + 9 x^{4} + 18 x^{3} + 3 x^{2} \cdot - 2 + 1 (3 x^{2}) + 1 (6 x) + 1 \cdot - 2$

Multiply $- 2$ by $3$ .

$3 x^{5} + 6 x^{4} - 2 x^{3} + 9 x^{4} + 18 x^{3} - 6 x^{2} + 1 (3 x^{2}) + 1 (6 x) + 1 \cdot - 2$

Multiply $3 x^{2}$ by $1$ .

$3 x^{5} + 6 x^{4} - 2 x^{3} + 9 x^{4} + 18 x^{3} - 6 x^{2} + 3 x^{2} + 1 (6 x) + 1 \cdot - 2$

Multiply $6 x$ by $1$ .

$3 x^{5} + 6 x^{4} - 2 x^{3} + 9 x^{4} + 18 x^{3} - 6 x^{2} + 3 x^{2} + 6 x + 1 \cdot - 2$

Multiply $- 2$ by $1$ .

$3 x^{5} + 6 x^{4} - 2 x^{3} + 9 x^{4} + 18 x^{3} - 6 x^{2} + 3 x^{2} + 6 x - 2$

Simplify by adding terms.

Add $6 x^{4}$ and $9 x^{4}$ .

$3 x^{5} + 15 x^{4} - 2 x^{3} + 18 x^{3} - 6 x^{2} + 3 x^{2} + 6 x - 2$

Add $- 2 x^{3}$ and $18 x^{3}$ .

$3 x^{5} + 15 x^{4} + 16 x^{3} - 6 x^{2} + 3 x^{2} + 6 x - 2$

Add $- 6 x^{2}$ and $3 x^{2}$ .

$3 x^{5} + 15 x^{4} + 16 x^{3} - 3 x^{2} + 6 x - 2$

Simplify (x^3+3x^2+1)(3x^2+6x-2)

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