Basic Math Examples

$(7 v^{2} - 6) \cdot (7 v^{2} + 6)$

Step 1

Expand $(7 v^{2} - 6) (7 v^{2} + 6)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$7 v^{2} (7 v^{2} + 6) - 6 (7 v^{2} + 6)$

Step 1.2

Apply the distributive property.

$7 v^{2} (7 v^{2}) + 7 v^{2} \cdot 6 - 6 (7 v^{2} + 6)$

Step 1.3

Apply the distributive property.

$7 v^{2} (7 v^{2}) + 7 v^{2} \cdot 6 - 6 (7 v^{2}) - 6 \cdot 6$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $7 v^{2} (7 v^{2}) + 7 v^{2} \cdot 6 - 6 (7 v^{2}) - 6 \cdot 6$ .

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Step 2.1.1

Reorder the factors in the terms $7 v^{2} \cdot 6$ and $- 6 (7 v^{2})$ .

$7 v^{2} (7 v^{2}) + 6 \cdot 7 v^{2} - 6 \cdot 7 v^{2} - 6 \cdot 6$

Step 2.1.2

Subtract $6 \cdot 7 v^{2}$ from $6 \cdot 7 v^{2}$ .

$7 v^{2} (7 v^{2}) + 0 - 6 \cdot 6$

Step 2.1.3

Add $7 v^{2} (7 v^{2})$ and $0$ .

$7 v^{2} (7 v^{2}) - 6 \cdot 6$

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

$7 \cdot 7 v^{2} v^{2} - 6 \cdot 6$

Step 2.2.2

Multiply $v^{2}$ by $v^{2}$ by adding the exponents.

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Step 2.2.2.1

Move $v^{2}$ .

$7 \cdot 7 (v^{2} v^{2}) - 6 \cdot 6$

Step 2.2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$7 \cdot 7 v^{2 + 2} - 6 \cdot 6$

Step 2.2.2.3

Add $2$ and $2$ .

$7 \cdot 7 v^{4} - 6 \cdot 6$

Step 2.2.3

Multiply $7$ by $7$ .

$49 v^{4} - 6 \cdot 6$

Step 2.2.4

Multiply $- 6$ by $6$ .

$49 v^{4} - 36$