Algebra Examples

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

Step 1

Apply the distributive property.

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

Step 2

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

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Step 2.1

Move $d^{3}$ .

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.3

Add $3$ and $1$ .

$4 d^{4} + 4 d (- d^{2})$

Step 3

Rewrite using the commutative property of multiplication.

$4 d^{4} + 4 \cdot - 1 d \cdot d^{2}$

Step 4

Simplify each term.

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Step 4.1

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

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Step 4.1.1

Move $d^{2}$ .

$4 d^{4} + 4 \cdot - 1 (d^{2} d)$

Step 4.1.2

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

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Step 4.1.2.1

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

$4 d^{4} + 4 \cdot - 1 (d^{2} d^{1})$

Step 4.1.2.2

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

$4 d^{4} + 4 \cdot - 1 d^{2 + 1}$

Step 4.1.3

Add $2$ and $1$ .

$4 d^{4} + 4 \cdot - 1 d^{3}$

Step 4.2

Multiply $4$ by $- 1$ .

$4 d^{4} - 4 d^{3}$