Pre-Algebra Examples

$(3 p + 2) (3 p - 2)$

Step 1

Expand $(3 p + 2) (3 p - 2)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$3 p (3 p - 2) + 2 (3 p - 2)$

Step 1.2

Apply the distributive property.

$3 p (3 p) + 3 p \cdot - 2 + 2 (3 p - 2)$

Step 1.3

Apply the distributive property.

$3 p (3 p) + 3 p \cdot - 2 + 2 (3 p) + 2 \cdot - 2$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $3 p (3 p) + 3 p \cdot - 2 + 2 (3 p) + 2 \cdot - 2$ .

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Step 2.1.1

Reorder the factors in the terms $3 p \cdot - 2$ and $2 (3 p)$ .

$3 p (3 p) - 2 \cdot 3 p + 2 \cdot 3 p + 2 \cdot - 2$

Step 2.1.2

Add $- 2 \cdot 3 p$ and $2 \cdot 3 p$ .

$3 p (3 p) + 0 + 2 \cdot - 2$

Step 2.1.3

Add $3 p (3 p)$ and $0$ .

$3 p (3 p) + 2 \cdot - 2$

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

$3 \cdot 3 p \cdot p + 2 \cdot - 2$

Step 2.2.2

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

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Step 2.2.2.1

Move $p$ .

$3 \cdot 3 (p \cdot p) + 2 \cdot - 2$

Step 2.2.2.2

Multiply $p$ by $p$ .

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

Step 2.2.3

Multiply $3$ by $3$ .

$9 p^{2} + 2 \cdot - 2$

Step 2.2.4

Multiply $2$ by $- 2$ .

$9 p^{2} - 4$