Algebra Examples

$(3 x + 1) (3 x - 1)$

Step 1

Expand $(3 x + 1) (3 x - 1)$ using the FOIL Method.

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Apply the distributive property.

$3 x (3 x - 1) + 1 (3 x - 1)$

Apply the distributive property.

$3 x (3 x) + 3 x \cdot - 1 + 1 (3 x - 1)$

Apply the distributive property.

$3 x (3 x) + 3 x \cdot - 1 + 1 (3 x) + 1 \cdot - 1$

Step 2

Simplify terms.

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Combine the opposite terms in $3 x (3 x) + 3 x \cdot - 1 + 1 (3 x) + 1 \cdot - 1$ .

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Reorder the factors in the terms $3 x \cdot - 1$ and $1 (3 x)$ .

$3 x (3 x) - 1 \cdot 3 x + 1 \cdot 3 x + 1 \cdot - 1$

Add $- 1 \cdot 3 x$ and $1 \cdot 3 x$ .

$3 x (3 x) + 0 + 1 \cdot - 1$

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

$3 x (3 x) + 1 \cdot - 1$

Simplify each term.

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Rewrite using the commutative property of multiplication.

$3 \cdot 3 x \cdot x + 1 \cdot - 1$

Multiply $x$ by $x$ by adding the exponents.

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Move $x$ .

$3 \cdot 3 (x \cdot x) + 1 \cdot - 1$

Multiply $x$ by $x$ .

$3 \cdot 3 x^{2} + 1 \cdot - 1$

Multiply $3$ by $3$ .

$9 x^{2} + 1 \cdot - 1$

Multiply $- 1$ by $1$ .

$9 x^{2} - 1$