Algebra Examples

$(a - 2) (4 a^{3} - 3 a^{2})$

Step 1

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

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Step 1.1

Apply the distributive property.

$a (4 a^{3} - 3 a^{2}) - 2 (4 a^{3} - 3 a^{2})$

Step 1.2

Apply the distributive property.

$a (4 a^{3}) + a (- 3 a^{2}) - 2 (4 a^{3} - 3 a^{2})$

Step 1.3

Apply the distributive property.

$a (4 a^{3}) + a (- 3 a^{2}) - 2 (4 a^{3}) - 2 (- 3 a^{2})$

Step 2

Simplify and combine like 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.

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

Step 2.1.2

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

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Step 2.1.2.1

Move $a^{3}$ .

$4 (a^{3} a) + a (- 3 a^{2}) - 2 (4 a^{3}) - 2 (- 3 a^{2})$

Step 2.1.2.2

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

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Step 2.1.2.2.1

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

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

Step 2.1.2.2.2

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

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

Step 2.1.2.3

Add $3$ and $1$ .

$4 a^{4} + a (- 3 a^{2}) - 2 (4 a^{3}) - 2 (- 3 a^{2})$

Step 2.1.3

Rewrite using the commutative property of multiplication.

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

Step 2.1.4

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

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Step 2.1.4.1

Move $a^{2}$ .

$4 a^{4} - 3 (a^{2} a) - 2 (4 a^{3}) - 2 (- 3 a^{2})$

Step 2.1.4.2

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

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Step 2.1.4.2.1

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

$4 a^{4} - 3 (a^{2} a^{1}) - 2 (4 a^{3}) - 2 (- 3 a^{2})$

Step 2.1.4.2.2

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

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

Step 2.1.4.3

Add $2$ and $1$ .

$4 a^{4} - 3 a^{3} - 2 (4 a^{3}) - 2 (- 3 a^{2})$

Step 2.1.5

Multiply $4$ by $- 2$ .

$4 a^{4} - 3 a^{3} - 8 a^{3} - 2 (- 3 a^{2})$

Step 2.1.6

Multiply $- 3$ by $- 2$ .

$4 a^{4} - 3 a^{3} - 8 a^{3} + 6 a^{2}$

Step 2.2

Subtract $8 a^{3}$ from $- 3 a^{3}$ .

$4 a^{4} - 11 a^{3} + 6 a^{2}$