Find the Product (x^2-2x-8)(-x^2+3x-5)

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

Expand $(x^{2} - 2 x - 8) (- x^{2} + 3 x - 5)$ by multiplying each term in the first expression by each term in the second expression.

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

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

$- x^{4} + 3 (x^{1} x^{2}) + x^{2} \cdot - 5 - 2 x (- x^{2}) - 2 x (3 x) - 2 x \cdot - 5 - 8 (- x^{2}) - 8 (3 x) - 8 \cdot - 5$

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

$- x^{4} + 3 x^{1 + 2} + x^{2} \cdot - 5 - 2 x (- x^{2}) - 2 x (3 x) - 2 x \cdot - 5 - 8 (- x^{2}) - 8 (3 x) - 8 \cdot - 5$

Add $1$ and $2$ .

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

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

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

Rewrite using the commutative property of multiplication.

$- x^{4} + 3 x^{3} - 5 x^{2} - 2 \cdot - 1 x \cdot x^{2} - 2 x (3 x) - 2 x \cdot - 5 - 8 (- x^{2}) - 8 (3 x) - 8 \cdot - 5$

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

Move $x^{2}$ .

$- x^{4} + 3 x^{3} - 5 x^{2} - 2 \cdot - 1 (x^{2} x) - 2 x (3 x) - 2 x \cdot - 5 - 8 (- x^{2}) - 8 (3 x) - 8 \cdot - 5$

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

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

$- x^{4} + 3 x^{3} - 5 x^{2} - 2 \cdot - 1 (x^{2} x^{1}) - 2 x (3 x) - 2 x \cdot - 5 - 8 (- x^{2}) - 8 (3 x) - 8 \cdot - 5$

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

$- x^{4} + 3 x^{3} - 5 x^{2} - 2 \cdot - 1 x^{2 + 1} - 2 x (3 x) - 2 x \cdot - 5 - 8 (- x^{2}) - 8 (3 x) - 8 \cdot - 5$

Add $2$ and $1$ .

$- x^{4} + 3 x^{3} - 5 x^{2} - 2 \cdot - 1 x^{3} - 2 x (3 x) - 2 x \cdot - 5 - 8 (- x^{2}) - 8 (3 x) - 8 \cdot - 5$

Multiply $- 2$ by $- 1$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $- 2$ by $3$ .

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

Multiply $- 5$ by $- 2$ .

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

Multiply $- 1$ by $- 8$ .

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

Multiply $3$ by $- 8$ .

$- x^{4} + 3 x^{3} - 5 x^{2} + 2 x^{3} - 6 x^{2} + 10 x + 8 x^{2} - 24 x - 8 \cdot - 5$

Multiply $- 8$ by $- 5$ .

$- x^{4} + 3 x^{3} - 5 x^{2} + 2 x^{3} - 6 x^{2} + 10 x + 8 x^{2} - 24 x + 40$

Simplify by adding terms.

Add $3 x^{3}$ and $2 x^{3}$ .

$- x^{4} + 5 x^{3} - 5 x^{2} - 6 x^{2} + 10 x + 8 x^{2} - 24 x + 40$

Subtract $6 x^{2}$ from $- 5 x^{2}$ .

$- x^{4} + 5 x^{3} - 11 x^{2} + 10 x + 8 x^{2} - 24 x + 40$

Add $- 11 x^{2}$ and $8 x^{2}$ .

$- x^{4} + 5 x^{3} - 3 x^{2} + 10 x - 24 x + 40$

Subtract $24 x$ from $10 x$ .

$- x^{4} + 5 x^{3} - 3 x^{2} - 14 x + 40$

Find the Product (x^2-2x-8)(-x^2+3x-5)

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