Algebra Examples

$(3 b + 1) (3 b - 1) - (b + 12)$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Apply the distributive property.

$3 b (3 b - 1) + 1 (3 b - 1) - (b + 12)$

Step 1.1.2

Apply the distributive property.

$3 b (3 b) + 3 b \cdot - 1 + 1 (3 b - 1) - (b + 12)$

Step 1.1.3

Apply the distributive property.

$3 b (3 b) + 3 b \cdot - 1 + 1 (3 b) + 1 \cdot - 1 - (b + 12)$

Step 1.2

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

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Step 1.2.1

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

$3 b (3 b) - 1 \cdot 3 b + 1 \cdot 3 b + 1 \cdot - 1 - (b + 12)$

Step 1.2.2

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

$3 b (3 b) + 0 + 1 \cdot - 1 - (b + 12)$

Step 1.2.3

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

$3 b (3 b) + 1 \cdot - 1 - (b + 12)$

Step 1.3

Simplify each term.

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Step 1.3.1

Rewrite using the commutative property of multiplication.

$3 \cdot 3 b \cdot b + 1 \cdot - 1 - (b + 12)$

Step 1.3.2

Multiply $b$ by $b$ by adding the exponents.

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Step 1.3.2.1

Move $b$ .

$3 \cdot 3 (b \cdot b) + 1 \cdot - 1 - (b + 12)$

Step 1.3.2.2

Multiply $b$ by $b$ .

$3 \cdot 3 b^{2} + 1 \cdot - 1 - (b + 12)$

Step 1.3.3

Multiply $3$ by $3$ .

$9 b^{2} + 1 \cdot - 1 - (b + 12)$

Step 1.3.4

Multiply $- 1$ by $1$ .

$9 b^{2} - 1 - (b + 12)$

Step 1.4

Apply the distributive property.

$9 b^{2} - 1 - b - 1 \cdot 12$

Step 1.5

Multiply $- 1$ by $12$ .

$9 b^{2} - 1 - b - 12$

Step 2

Subtract $12$ from $- 1$ .

$9 b^{2} - b - 13$