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

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

Expand $(- 4 x^{4} - 3 x^{3}) (- 9 x^{2} + x)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

$- 4 x^{4} (- 9 x^{2}) - 4 x^{4} x - 3 x^{3} (- 9 x^{2}) - 3 x^{3} x$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

Multiply $x^{4}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

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

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

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

Add $2$ and $4$ .

$- 4 \cdot - 9 x^{6} - 4 x^{4} x - 3 x^{3} (- 9 x^{2}) - 3 x^{3} x$

Multiply $- 4$ by $- 9$ .

$36 x^{6} - 4 x^{4} x - 3 x^{3} (- 9 x^{2}) - 3 x^{3} x$

Multiply $x^{4}$ by $x$ by adding the exponents.

Move $x$ .

$36 x^{6} - 4 (x \cdot x^{4}) - 3 x^{3} (- 9 x^{2}) - 3 x^{3} x$

Multiply $x$ by $x^{4}$ .

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

$36 x^{6} - 4 (x^{1} x^{4}) - 3 x^{3} (- 9 x^{2}) - 3 x^{3} x$

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

$36 x^{6} - 4 x^{1 + 4} - 3 x^{3} (- 9 x^{2}) - 3 x^{3} x$

Add $1$ and $4$ .

$36 x^{6} - 4 x^{5} - 3 x^{3} (- 9 x^{2}) - 3 x^{3} x$

Rewrite using the commutative property of multiplication.

$36 x^{6} - 4 x^{5} - 3 \cdot - 9 x^{3} x^{2} - 3 x^{3} x$

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

Move $x^{2}$ .

$36 x^{6} - 4 x^{5} - 3 \cdot - 9 (x^{2} x^{3}) - 3 x^{3} x$

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

$36 x^{6} - 4 x^{5} - 3 \cdot - 9 x^{2 + 3} - 3 x^{3} x$

Add $2$ and $3$ .

$36 x^{6} - 4 x^{5} - 3 \cdot - 9 x^{5} - 3 x^{3} x$

Multiply $- 3$ by $- 9$ .

$36 x^{6} - 4 x^{5} + 27 x^{5} - 3 x^{3} x$

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

Move $x$ .

$36 x^{6} - 4 x^{5} + 27 x^{5} - 3 (x \cdot x^{3})$

Multiply $x$ by $x^{3}$ .

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

$36 x^{6} - 4 x^{5} + 27 x^{5} - 3 (x^{1} x^{3})$

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

$36 x^{6} - 4 x^{5} + 27 x^{5} - 3 x^{1 + 3}$

Add $1$ and $3$ .

$36 x^{6} - 4 x^{5} + 27 x^{5} - 3 x^{4}$

Add $- 4 x^{5}$ and $27 x^{5}$ .

$36 x^{6} + 23 x^{5} - 3 x^{4}$

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

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