Write in Standard Form (x^2-2x-3)(2x^2+4x-5)

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

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

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

Expand $(x^{2} - 2 x - 3) (2 x^{2} + 4 x - 5)$ by multiplying each term in the first expression by each term in the second expression.

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

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Move $- 5$ to the left of $x^{2}$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $- 2$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 2$ by $4$ .

$2 x^{4} + 4 x^{3} - 5 x^{2} - 4 x^{3} - 8 x^{2} - 2 x \cdot - 5 - 3 (2 x^{2}) - 3 (4 x) - 3 \cdot - 5$

Multiply $- 5$ by $- 2$ .

$2 x^{4} + 4 x^{3} - 5 x^{2} - 4 x^{3} - 8 x^{2} + 10 x - 3 (2 x^{2}) - 3 (4 x) - 3 \cdot - 5$

Multiply $2$ by $- 3$ .

$2 x^{4} + 4 x^{3} - 5 x^{2} - 4 x^{3} - 8 x^{2} + 10 x - 6 x^{2} - 3 (4 x) - 3 \cdot - 5$

Multiply $4$ by $- 3$ .

$2 x^{4} + 4 x^{3} - 5 x^{2} - 4 x^{3} - 8 x^{2} + 10 x - 6 x^{2} - 12 x - 3 \cdot - 5$

Multiply $- 3$ by $- 5$ .

$2 x^{4} + 4 x^{3} - 5 x^{2} - 4 x^{3} - 8 x^{2} + 10 x - 6 x^{2} - 12 x + 15$

Simplify by adding terms.

Combine the opposite terms in $2 x^{4} + 4 x^{3} - 5 x^{2} - 4 x^{3} - 8 x^{2} + 10 x - 6 x^{2} - 12 x + 15$ .

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

$2 x^{4} - 5 x^{2} + 0 - 8 x^{2} + 10 x - 6 x^{2} - 12 x + 15$

Add $2 x^{4} - 5 x^{2}$ and $0$ .

$2 x^{4} - 5 x^{2} - 8 x^{2} + 10 x - 6 x^{2} - 12 x + 15$

Subtract $8 x^{2}$ from $- 5 x^{2}$ .

$2 x^{4} - 13 x^{2} + 10 x - 6 x^{2} - 12 x + 15$

Subtract $6 x^{2}$ from $- 13 x^{2}$ .

$2 x^{4} - 19 x^{2} + 10 x - 12 x + 15$

Subtract $12 x$ from $10 x$ .

$2 x^{4} - 19 x^{2} - 2 x + 15$

Write in Standard Form (x^2-2x-3)(2x^2+4x-5)

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