Write in Standard Form (2x^2-9x-9)(2x^2-x+1)

$(2 x^{2} - 9 x - 9) (2 x^{2} - x + 1)$

Step 1

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

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

Step 2

Expand $(2 x^{2} - 9 x - 9) (2 x^{2} - x + 1)$ by multiplying each term in the first expression by each term in the second expression.

$2 x^{2} (2 x^{2}) + 2 x^{2} (- x) + 2 x^{2} \cdot 1 - 9 x (2 x^{2}) - 9 x (- x) - 9 x \cdot 1 - 9 (2 x^{2}) - 9 (- x) - 9 \cdot 1$

Step 3

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x^{2} x^{2} + 2 x^{2} (- x) + 2 x^{2} \cdot 1 - 9 x (2 x^{2}) - 9 x (- x) - 9 x \cdot 1 - 9 (2 x^{2}) - 9 (- x) - 9 \cdot 1$

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

Move $x^{2}$ .

$2 \cdot 2 (x^{2} x^{2}) + 2 x^{2} (- x) + 2 x^{2} \cdot 1 - 9 x (2 x^{2}) - 9 x (- x) - 9 x \cdot 1 - 9 (2 x^{2}) - 9 (- x) - 9 \cdot 1$

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

$2 \cdot 2 x^{2 + 2} + 2 x^{2} (- x) + 2 x^{2} \cdot 1 - 9 x (2 x^{2}) - 9 x (- x) - 9 x \cdot 1 - 9 (2 x^{2}) - 9 (- x) - 9 \cdot 1$

Add $2$ and $2$ .

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

Multiply $2$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $2$ by $- 1$ .

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

Multiply $2$ by $1$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $- 9$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 9$ by $- 1$ .

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

Multiply $- 9$ by $1$ .

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

Multiply $2$ by $- 9$ .

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

Multiply $- 1$ by $- 9$ .

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

Multiply $- 9$ by $1$ .

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

Simplify by adding terms.

Combine the opposite terms in $4 x^{4} - 2 x^{3} + 2 x^{2} - 18 x^{3} + 9 x^{2} - 9 x - 18 x^{2} + 9 x - 9$ .

Add $- 9 x$ and $9 x$ .

$4 x^{4} - 2 x^{3} + 2 x^{2} - 18 x^{3} + 9 x^{2} - 18 x^{2} + 0 - 9$

Add $4 x^{4} - 2 x^{3} + 2 x^{2} - 18 x^{3} + 9 x^{2} - 18 x^{2}$ and $0$ .

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

Subtract $18 x^{3}$ from $- 2 x^{3}$ .

$4 x^{4} - 20 x^{3} + 2 x^{2} + 9 x^{2} - 18 x^{2} - 9$

Add $2 x^{2}$ and $9 x^{2}$ .

$4 x^{4} - 20 x^{3} + 11 x^{2} - 18 x^{2} - 9$

Subtract $18 x^{2}$ from $11 x^{2}$ .

$4 x^{4} - 20 x^{3} - 7 x^{2} - 9$

Write in Standard Form (2x^2-9x-9)(2x^2-x+1)

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