Basic Math Examples

$(4 n + 1) (4 n - 1)$

Step 1

Expand

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

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Step 1.1

Apply the distributive property.

$4 n (4 n - 1) + 1 (4 n - 1)$

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in

$4 n (4 n) + 4 n \cdot - 1 + 1 (4 n) + 1 \cdot - 1$ .

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Step 2.1.1

Reorder the factors in the terms

$4 n \cdot - 1$ and

$1 (4 n)$ .

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

Step 2.1.2

Add

$- 1 \cdot 4 n$ and

$1 \cdot 4 n$ .

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

Step 2.1.3

Add

$4 n (4 n)$ and

$0$ .

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

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

$4 \cdot 4 n \cdot n + 1 \cdot - 1$

Step 2.2.2

Multiply

$n$ by

$n$ by adding the exponents.

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Step 2.2.2.1

Move

$n$ .

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

Step 2.2.2.2

Multiply

$n$ by

$n$ .

$4 \cdot 4 n^{2} + 1 \cdot - 1$

Step 2.2.3

Multiply

$4$ by

$4$ .

$16 n^{2} + 1 \cdot - 1$

Step 2.2.4

Multiply

$- 1$ by

$1$ .

$16 n^{2} - 1$