Write in Standard Form (2x^2-x-2)(x^2-6x+4)

$(2 x^{2} - x - 2) (x^{2} - 6 x + 4)$

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

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

Expand $(2 x^{2} - x - 2) (x^{2} - 6 x + 4)$ by multiplying each term in the first expression by each term in the second expression.

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

Simplify terms.

Simplify each term.

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $2$ by $- 6$ .

$2 x^{4} - 12 x^{3} + 2 x^{2} \cdot 4 - x \cdot x^{2} - x (- 6 x) - x \cdot 4 - 2 x^{2} - 2 (- 6 x) - 2 \cdot 4$

Multiply $4$ by $2$ .

$2 x^{4} - 12 x^{3} + 8 x^{2} - x \cdot x^{2} - x (- 6 x) - x \cdot 4 - 2 x^{2} - 2 (- 6 x) - 2 \cdot 4$

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

Move $x^{2}$ .

$2 x^{4} - 12 x^{3} + 8 x^{2} - (x^{2} x) - x (- 6 x) - x \cdot 4 - 2 x^{2} - 2 (- 6 x) - 2 \cdot 4$

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

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

$2 x^{4} - 12 x^{3} + 8 x^{2} - (x^{2} x^{1}) - x (- 6 x) - x \cdot 4 - 2 x^{2} - 2 (- 6 x) - 2 \cdot 4$

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

$2 x^{4} - 12 x^{3} + 8 x^{2} - x^{2 + 1} - x (- 6 x) - x \cdot 4 - 2 x^{2} - 2 (- 6 x) - 2 \cdot 4$

Add $2$ and $1$ .

$2 x^{4} - 12 x^{3} + 8 x^{2} - x^{3} - x (- 6 x) - x \cdot 4 - 2 x^{2} - 2 (- 6 x) - 2 \cdot 4$

Rewrite using the commutative property of multiplication.

$2 x^{4} - 12 x^{3} + 8 x^{2} - x^{3} - 1 \cdot - 6 x \cdot x - x \cdot 4 - 2 x^{2} - 2 (- 6 x) - 2 \cdot 4$

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

Move $x$ .

$2 x^{4} - 12 x^{3} + 8 x^{2} - x^{3} - 1 \cdot - 6 (x \cdot x) - x \cdot 4 - 2 x^{2} - 2 (- 6 x) - 2 \cdot 4$

Multiply $x$ by $x$ .

$2 x^{4} - 12 x^{3} + 8 x^{2} - x^{3} - 1 \cdot - 6 x^{2} - x \cdot 4 - 2 x^{2} - 2 (- 6 x) - 2 \cdot 4$

Multiply $- 1$ by $- 6$ .

$2 x^{4} - 12 x^{3} + 8 x^{2} - x^{3} + 6 x^{2} - x \cdot 4 - 2 x^{2} - 2 (- 6 x) - 2 \cdot 4$

Multiply $4$ by $- 1$ .

$2 x^{4} - 12 x^{3} + 8 x^{2} - x^{3} + 6 x^{2} - 4 x - 2 x^{2} - 2 (- 6 x) - 2 \cdot 4$

Multiply $- 6$ by $- 2$ .

$2 x^{4} - 12 x^{3} + 8 x^{2} - x^{3} + 6 x^{2} - 4 x - 2 x^{2} + 12 x - 2 \cdot 4$

Multiply $- 2$ by $4$ .

$2 x^{4} - 12 x^{3} + 8 x^{2} - x^{3} + 6 x^{2} - 4 x - 2 x^{2} + 12 x - 8$

Simplify by adding terms.

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

$2 x^{4} - 13 x^{3} + 8 x^{2} + 6 x^{2} - 4 x - 2 x^{2} + 12 x - 8$

Add $8 x^{2}$ and $6 x^{2}$ .

$2 x^{4} - 13 x^{3} + 14 x^{2} - 4 x - 2 x^{2} + 12 x - 8$

Subtract $2 x^{2}$ from $14 x^{2}$ .

$2 x^{4} - 13 x^{3} + 12 x^{2} - 4 x + 12 x - 8$

Add $- 4 x$ and $12 x$ .

$2 x^{4} - 13 x^{3} + 12 x^{2} + 8 x - 8$

Write in Standard Form (2x^2-x-2)(x^2-6x+4)

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