Find the Product (5a-3a^3)(4a-1)

$(5 a - 3 a^{3}) (4 a - 1)$

Expand $(5 a - 3 a^{3}) (4 a - 1)$ using the FOIL Method.

Apply the distributive property.

$5 a (4 a - 1) - 3 a^{3} (4 a - 1)$

Apply the distributive property.

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

Apply the distributive property.

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

Simplify each term.

Rewrite using the commutative property of multiplication.

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

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

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

Multiply $a$ by $a$ .

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

Multiply $5$ by $4$ .

$20 a^{2} + 5 a \cdot - 1 - 3 a^{3} (4 a) - 3 a^{3} \cdot - 1$

Multiply $- 1$ by $5$ .

$20 a^{2} - 5 a - 3 a^{3} (4 a) - 3 a^{3} \cdot - 1$

Rewrite using the commutative property of multiplication.

$20 a^{2} - 5 a - 3 \cdot 4 a^{3} a - 3 a^{3} \cdot - 1$

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

Move $a$ .

$20 a^{2} - 5 a - 3 \cdot 4 (a \cdot a^{3}) - 3 a^{3} \cdot - 1$

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

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

$20 a^{2} - 5 a - 3 \cdot 4 (a^{1} a^{3}) - 3 a^{3} \cdot - 1$

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

$20 a^{2} - 5 a - 3 \cdot 4 a^{1 + 3} - 3 a^{3} \cdot - 1$

Add $1$ and $3$ .

$20 a^{2} - 5 a - 3 \cdot 4 a^{4} - 3 a^{3} \cdot - 1$

Multiply $- 3$ by $4$ .

$20 a^{2} - 5 a - 12 a^{4} - 3 a^{3} \cdot - 1$

Multiply $- 1$ by $- 3$ .

$20 a^{2} - 5 a - 12 a^{4} + 3 a^{3}$