Basic Math Examples

$(7 x - 1) (7 x + 1)$

Step 1

Expand $(7 x - 1) (7 x + 1)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$7 x (7 x + 1) - 1 (7 x + 1)$

Step 1.2

Apply the distributive property.

$7 x (7 x) + 7 x \cdot 1 - 1 (7 x + 1)$

Step 1.3

Apply the distributive property.

$7 x (7 x) + 7 x \cdot 1 - 1 (7 x) - 1 \cdot 1$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $7 x (7 x) + 7 x \cdot 1 - 1 (7 x) - 1 \cdot 1$ .

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Step 2.1.1

Reorder the factors in the terms $7 x \cdot 1$ and $- 1 (7 x)$ .

$7 x (7 x) + 1 \cdot 7 x - 1 \cdot 7 x - 1 \cdot 1$

Step 2.1.2

Subtract $7 x$ from $1 \cdot 7 x$ .

$7 x (7 x) + 0 - 1 \cdot 1$

Step 2.1.3

Add $7 x (7 x)$ and $0$ .

$7 x (7 x) - 1 \cdot 1$

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

$7 \cdot 7 x \cdot x - 1 \cdot 1$

Step 2.2.2

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

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Step 2.2.2.1

Move $x$ .

$7 \cdot 7 (x \cdot x) - 1 \cdot 1$

Step 2.2.2.2

Multiply $x$ by $x$ .

$7 \cdot 7 x^{2} - 1 \cdot 1$

Step 2.2.3

Multiply $7$ by $7$ .

$49 x^{2} - 1 \cdot 1$

Step 2.2.4

Multiply $- 1$ by $1$ .

$49 x^{2} - 1$