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

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

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

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

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

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

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

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

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

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

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

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

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

Add $2$ and $1$ .

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

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

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

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $2$ by $2$ .

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $2$ by $1$ .

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

Multiply $2$ by $- 2$ .

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

Multiply $- 2$ by $1$ .

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

Simplify by adding terms.

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

Subtract $2 x$ from $2 x$ .

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

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

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

Add $x^{3}$ and $4 x^{3}$ .

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

Add $x^{2}$ and $2 x^{2}$ .

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

Subtract $4 x^{2}$ from $3 x^{2}$ .

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

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

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