Finite Math Examples

$(8 m + 1) (8 m - 1)$

Step 1

Expand $(8 m + 1) (8 m - 1)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$8 m (8 m - 1) + 1 (8 m - 1)$

Step 1.2

Apply the distributive property.

$8 m (8 m) + 8 m \cdot - 1 + 1 (8 m - 1)$

Step 1.3

Apply the distributive property.

$8 m (8 m) + 8 m \cdot - 1 + 1 (8 m) + 1 \cdot - 1$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $8 m (8 m) + 8 m \cdot - 1 + 1 (8 m) + 1 \cdot - 1$ .

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Step 2.1.1

Reorder the factors in the terms $8 m \cdot - 1$ and $1 (8 m)$ .

$8 m (8 m) - 1 \cdot 8 m + 1 \cdot 8 m + 1 \cdot - 1$

Step 2.1.2

Add $- 1 \cdot 8 m$ and $1 \cdot 8 m$ .

$8 m (8 m) + 0 + 1 \cdot - 1$

Step 2.1.3

Add $8 m (8 m)$ and $0$ .

$8 m (8 m) + 1 \cdot - 1$

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

$8 \cdot 8 m \cdot m + 1 \cdot - 1$

Step 2.2.2

Multiply $m$ by $m$ by adding the exponents.

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Step 2.2.2.1

Move $m$ .

$8 \cdot 8 (m \cdot m) + 1 \cdot - 1$

Step 2.2.2.2

Multiply $m$ by $m$ .

$8 \cdot 8 m^{2} + 1 \cdot - 1$

Step 2.2.3

Multiply $8$ by $8$ .

$64 m^{2} + 1 \cdot - 1$

Step 2.2.4

Multiply $- 1$ by $1$ .

$64 m^{2} - 1$

Step 3

Rewrite $64 m^{2}$ as ${(8 m)}^{2}$ .

${(8 m)}^{2} - 1$

Step 4

Rewrite $1$ as $1^{2}$ .

${(8 m)}^{2} - 1^{2}$

Step 5

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 8 m$ and $b = 1$ .

$(8 m + 1) (8 m - 1)$