Find the Product (-2x^2+5)(x^3-8x-6)

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

Expand $(- 2 x^{2} + 5) (x^{3} - 8 x - 6)$ by multiplying each term in the first expression by each term in the second expression.

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

Simplify terms.

Simplify each term.

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

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

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

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

Add $3$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

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

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

$- 2 x^{5} - 2 \cdot - 8 (x^{1} x^{2}) - 2 x^{2} \cdot - 6 + 5 x^{3} + 5 (- 8 x) + 5 \cdot - 6$

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

$- 2 x^{5} - 2 \cdot - 8 x^{1 + 2} - 2 x^{2} \cdot - 6 + 5 x^{3} + 5 (- 8 x) + 5 \cdot - 6$

Add $1$ and $2$ .

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

Multiply $- 2$ by $- 8$ .

$- 2 x^{5} + 16 x^{3} - 2 x^{2} \cdot - 6 + 5 x^{3} + 5 (- 8 x) + 5 \cdot - 6$

Multiply $- 6$ by $- 2$ .

$- 2 x^{5} + 16 x^{3} + 12 x^{2} + 5 x^{3} + 5 (- 8 x) + 5 \cdot - 6$

Multiply $- 8$ by $5$ .

$- 2 x^{5} + 16 x^{3} + 12 x^{2} + 5 x^{3} - 40 x + 5 \cdot - 6$

Multiply $5$ by $- 6$ .

$- 2 x^{5} + 16 x^{3} + 12 x^{2} + 5 x^{3} - 40 x - 30$

Add $16 x^{3}$ and $5 x^{3}$ .

$- 2 x^{5} + 21 x^{3} + 12 x^{2} - 40 x - 30$