Finite Math Examples

$6 p^{2} {(1 - p)}^{2}$

Step 1

Rewrite ${(1 - p)}^{2}$ as $(1 - p) (1 - p)$ .

$6 p^{2} ((1 - p) (1 - p))$

Step 2

Expand $(1 - p) (1 - p)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$6 p^{2} (1 (1 - p) - p (1 - p))$

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $1$ by $1$ .

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

Step 3.1.2

Multiply $- p$ by $1$ .

$6 p^{2} (1 - p - p \cdot 1 - p (- p))$

Step 3.1.3

Multiply $- 1$ by $1$ .

$6 p^{2} (1 - p - p - p (- p))$

Step 3.1.4

Rewrite using the commutative property of multiplication.

$6 p^{2} (1 - p - p - 1 \cdot - 1 p \cdot p)$

Step 3.1.5

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

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Step 3.1.5.1

Move $p$ .

$6 p^{2} (1 - p - p - 1 \cdot - 1 (p \cdot p))$

Step 3.1.5.2

Multiply $p$ by $p$ .

$6 p^{2} (1 - p - p - 1 \cdot - 1 p^{2})$

Step 3.1.6

Multiply $- 1$ by $- 1$ .

$6 p^{2} (1 - p - p + 1 p^{2})$

Step 3.1.7

Multiply $p^{2}$ by $1$ .

$6 p^{2} (1 - p - p + p^{2})$

Step 3.2

Subtract $p$ from $- p$ .

$6 p^{2} (1 - 2 p + p^{2})$

Step 4

Apply the distributive property.

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

Step 5

Simplify.

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Step 5.1

Multiply $6$ by $1$ .

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

Step 5.2

Rewrite using the commutative property of multiplication.

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

Step 5.3

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

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Step 5.3.1

Move $p^{2}$ .

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

Step 5.3.2

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

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

Step 5.3.3

Add $2$ and $2$ .

$6 p^{2} + 6 \cdot - 2 p^{2} p + 6 p^{4}$

Step 6

Simplify each term.

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Step 6.1

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

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Step 6.1.1

Move $p$ .

$6 p^{2} + 6 \cdot - 2 (p \cdot p^{2}) + 6 p^{4}$

Step 6.1.2

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

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Step 6.1.2.1

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

$6 p^{2} + 6 \cdot - 2 (p^{1} p^{2}) + 6 p^{4}$

Step 6.1.2.2

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

$6 p^{2} + 6 \cdot - 2 p^{1 + 2} + 6 p^{4}$

Step 6.1.3

Add $1$ and $2$ .

$6 p^{2} + 6 \cdot - 2 p^{3} + 6 p^{4}$

Step 6.2

Multiply $6$ by $- 2$ .

$6 p^{2} - 12 p^{3} + 6 p^{4}$