Find the Product -4x^5(11x^3+2x^2+9x+1)

$- 4 x^{5} (11 x^{3} + 2 x^{2} + 9 x + 1)$

Apply the distributive property.

$- 4 x^{5} (11 x^{3}) - 4 x^{5} (2 x^{2}) - 4 x^{5} (9 x) - 4 x^{5} \cdot 1$

Simplify.

Rewrite using the commutative property of multiplication.

$- 4 \cdot 11 x^{5} x^{3} - 4 x^{5} (2 x^{2}) - 4 x^{5} (9 x) - 4 x^{5} \cdot 1$

Rewrite using the commutative property of multiplication.

$- 4 \cdot 11 x^{5} x^{3} - 4 \cdot 2 x^{5} x^{2} - 4 x^{5} (9 x) - 4 x^{5} \cdot 1$

Rewrite using the commutative property of multiplication.

$- 4 \cdot 11 x^{5} x^{3} - 4 \cdot 2 x^{5} x^{2} - 4 \cdot 9 x^{5} x - 4 x^{5} \cdot 1$

Multiply $- 4$ by $1$ .

$- 4 \cdot 11 x^{5} x^{3} - 4 \cdot 2 x^{5} x^{2} - 4 \cdot 9 x^{5} x - 4 x^{5}$

Simplify each term.

Multiply $x^{5}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$- 4 \cdot 11 (x^{3} x^{5}) - 4 \cdot 2 x^{5} x^{2} - 4 \cdot 9 x^{5} x - 4 x^{5}$

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

$- 4 \cdot 11 x^{3 + 5} - 4 \cdot 2 x^{5} x^{2} - 4 \cdot 9 x^{5} x - 4 x^{5}$

Add $3$ and $5$ .

$- 4 \cdot 11 x^{8} - 4 \cdot 2 x^{5} x^{2} - 4 \cdot 9 x^{5} x - 4 x^{5}$

Multiply $- 4$ by $11$ .

$- 44 x^{8} - 4 \cdot 2 x^{5} x^{2} - 4 \cdot 9 x^{5} x - 4 x^{5}$

Multiply $x^{5}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$- 44 x^{8} - 4 \cdot 2 (x^{2} x^{5}) - 4 \cdot 9 x^{5} x - 4 x^{5}$

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

$- 44 x^{8} - 4 \cdot 2 x^{2 + 5} - 4 \cdot 9 x^{5} x - 4 x^{5}$

Add $2$ and $5$ .

$- 44 x^{8} - 4 \cdot 2 x^{7} - 4 \cdot 9 x^{5} x - 4 x^{5}$

Multiply $- 4$ by $2$ .

$- 44 x^{8} - 8 x^{7} - 4 \cdot 9 x^{5} x - 4 x^{5}$

Multiply $x^{5}$ by $x$ by adding the exponents.

Move $x$ .

$- 44 x^{8} - 8 x^{7} - 4 \cdot 9 (x \cdot x^{5}) - 4 x^{5}$

Multiply $x$ by $x^{5}$ .

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

$- 44 x^{8} - 8 x^{7} - 4 \cdot 9 (x^{1} x^{5}) - 4 x^{5}$

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

$- 44 x^{8} - 8 x^{7} - 4 \cdot 9 x^{1 + 5} - 4 x^{5}$

Add $1$ and $5$ .

$- 44 x^{8} - 8 x^{7} - 4 \cdot 9 x^{6} - 4 x^{5}$

Multiply $- 4$ by $9$ .

$- 44 x^{8} - 8 x^{7} - 36 x^{6} - 4 x^{5}$