Algebra Examples

$8 p (- 3 p^{2} + 6 p - 2)$

Step 1

Apply the distributive property.

$8 p (- 3 p^{2}) + 8 p (6 p) + 8 p \cdot - 2$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$8 \cdot - 3 p \cdot p^{2} + 8 p (6 p) + 8 p \cdot - 2$

Step 2.2

Rewrite using the commutative property of multiplication.

$8 \cdot - 3 p \cdot p^{2} + 8 \cdot 6 p \cdot p + 8 p \cdot - 2$

Step 2.3

Multiply $- 2$ by $8$ .

$8 \cdot - 3 p \cdot p^{2} + 8 \cdot 6 p \cdot p - 16 p$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $p^{2}$ .

$8 \cdot - 3 (p^{2} p) + 8 \cdot 6 p \cdot p - 16 p$

Step 3.1.2

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

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Step 3.1.2.1

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

$8 \cdot - 3 (p^{2} p^{1}) + 8 \cdot 6 p \cdot p - 16 p$

Step 3.1.2.2

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

$8 \cdot - 3 p^{2 + 1} + 8 \cdot 6 p \cdot p - 16 p$

Step 3.1.3

Add $2$ and $1$ .

$8 \cdot - 3 p^{3} + 8 \cdot 6 p \cdot p - 16 p$

Step 3.2

Multiply $8$ by $- 3$ .

$- 24 p^{3} + 8 \cdot 6 p \cdot p - 16 p$

Step 3.3

Multiply $p$ by $p$ by adding the exponents.

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Step 3.3.1

Move $p$ .

$- 24 p^{3} + 8 \cdot 6 (p \cdot p) - 16 p$

Step 3.3.2

Multiply $p$ by $p$ .

$- 24 p^{3} + 8 \cdot 6 p^{2} - 16 p$

Step 3.4

Multiply $8$ by $6$ .

$- 24 p^{3} + 48 p^{2} - 16 p$