Write in Standard Form (x^2-4x-4)(3x^2+x-1)

$(x^{2} - 4 x - 4) (3 x^{2} + x - 1)$

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

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

Expand $(x^{2} - 4 x - 4) (3 x^{2} + x - 1)$ by multiplying each term in the first expression by each term in the second expression.

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

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

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

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

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

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

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

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

Add $2$ and $1$ .

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

Move $- 1$ to the left of $x^{2}$ .

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

Rewrite $- 1 x^{2}$ as $- x^{2}$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $- 4$ by $3$ .

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

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 1$ by $- 4$ .

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

Multiply $3$ by $- 4$ .

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

Multiply $- 4$ by $- 1$ .

$3 x^{4} + x^{3} - x^{2} - 12 x^{3} - 4 x^{2} + 4 x - 12 x^{2} - 4 x + 4$

Simplify by adding terms.

Combine the opposite terms in $3 x^{4} + x^{3} - x^{2} - 12 x^{3} - 4 x^{2} + 4 x - 12 x^{2} - 4 x + 4$ .

Subtract $4 x$ from $4 x$ .

$3 x^{4} + x^{3} - x^{2} - 12 x^{3} - 4 x^{2} - 12 x^{2} + 0 + 4$

Add $3 x^{4} + x^{3} - x^{2} - 12 x^{3} - 4 x^{2} - 12 x^{2}$ and $0$ .

$3 x^{4} + x^{3} - x^{2} - 12 x^{3} - 4 x^{2} - 12 x^{2} + 4$

Subtract $12 x^{3}$ from $x^{3}$ .

$3 x^{4} - 11 x^{3} - x^{2} - 4 x^{2} - 12 x^{2} + 4$

Subtract $4 x^{2}$ from $- x^{2}$ .

$3 x^{4} - 11 x^{3} - 5 x^{2} - 12 x^{2} + 4$

Subtract $12 x^{2}$ from $- 5 x^{2}$ .

$3 x^{4} - 11 x^{3} - 17 x^{2} + 4$

Write in Standard Form (x^2-4x-4)(3x^2+x-1)

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