Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

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

Step 2.1.2

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

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Step 2.1.2.1

Move $a$ .

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

Step 2.1.2.2

Multiply $a$ by $a$ .

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

Step 2.1.3

Multiply $5$ by $4$ .

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

Step 2.1.4

Multiply $- 1$ by $5$ .

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

Step 2.1.5

Rewrite using the commutative property of multiplication.

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

Step 2.1.6

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

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Step 2.1.6.1

Move $a$ .

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

Step 2.1.6.2

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

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Step 2.1.6.2.1

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

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

Step 2.1.6.2.2

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

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

Step 2.1.6.3

Add $1$ and $3$ .

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

Step 2.1.7

Multiply $- 3$ by $4$ .

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

Step 2.1.8

Multiply $- 1$ by $- 3$ .

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

Step 2.2

Reorder.

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Step 2.2.1

Move $- 5 a$ .

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

Step 2.2.2

Move $20 a^{2}$ .

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