Chemistry Examples

$(4 b - 1) (4 b + 1)$

Step 1

Expand $(4 b - 1) (4 b + 1)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$4 b (4 b + 1) - 1 (4 b + 1)$

Step 1.2

Apply the distributive property.

$4 b (4 b) + 4 b \cdot 1 - 1 (4 b + 1)$

Step 1.3

Apply the distributive property.

$4 b (4 b) + 4 b \cdot 1 - 1 (4 b) - 1 \cdot 1$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $4 b (4 b) + 4 b \cdot 1 - 1 (4 b) - 1 \cdot 1$ .

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Step 2.1.1

Reorder the factors in the terms $4 b \cdot 1$ and $- 1 (4 b)$ .

$4 b (4 b) + 1 \cdot 4 b - 1 \cdot 4 b - 1 \cdot 1$

Step 2.1.2

Subtract $4 b$ from $1 \cdot 4 b$ .

$4 b (4 b) + 0 - 1 \cdot 1$

Step 2.1.3

Add $4 b (4 b)$ and $0$ .

$4 b (4 b) - 1 \cdot 1$

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

$4 \cdot 4 b \cdot b - 1 \cdot 1$

Step 2.2.2

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

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Step 2.2.2.1

Move $b$ .

$4 \cdot 4 (b \cdot b) - 1 \cdot 1$

Step 2.2.2.2

Multiply $b$ by $b$ .

$4 \cdot 4 b^{2} - 1 \cdot 1$

Step 2.2.3

Multiply $4$ by $4$ .

$16 b^{2} - 1 \cdot 1$

Step 2.2.4

Multiply $- 1$ by $1$ .

$16 b^{2} - 1$