Algebra Examples

$(3 + 7 v^{2}) (3 - 7 v^{2})$

Step 1

Expand $(3 + 7 v^{2}) (3 - 7 v^{2})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$3 (3 - 7 v^{2}) + 7 v^{2} (3 - 7 v^{2})$

Step 1.2

Apply the distributive property.

$3 \cdot 3 + 3 (- 7 v^{2}) + 7 v^{2} (3 - 7 v^{2})$

Step 1.3

Apply the distributive property.

$3 \cdot 3 + 3 (- 7 v^{2}) + 7 v^{2} \cdot 3 + 7 v^{2} (- 7 v^{2})$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $3$ by $3$ .

$9 + 3 (- 7 v^{2}) + 7 v^{2} \cdot 3 + 7 v^{2} (- 7 v^{2})$

Step 2.1.2

Multiply $- 7$ by $3$ .

$9 - 21 v^{2} + 7 v^{2} \cdot 3 + 7 v^{2} (- 7 v^{2})$

Step 2.1.3

Multiply $3$ by $7$ .

$9 - 21 v^{2} + 21 v^{2} + 7 v^{2} (- 7 v^{2})$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$9 - 21 v^{2} + 21 v^{2} + 7 \cdot - 7 v^{2} v^{2}$

Step 2.1.5

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

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Step 2.1.5.1

Move $v^{2}$ .

$9 - 21 v^{2} + 21 v^{2} + 7 \cdot - 7 (v^{2} v^{2})$

Step 2.1.5.2

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

$9 - 21 v^{2} + 21 v^{2} + 7 \cdot - 7 v^{2 + 2}$

Step 2.1.5.3

Add $2$ and $2$ .

$9 - 21 v^{2} + 21 v^{2} + 7 \cdot - 7 v^{4}$

Step 2.1.6

Multiply $7$ by $- 7$ .

$9 - 21 v^{2} + 21 v^{2} - 49 v^{4}$

Step 2.2

Add $- 21 v^{2}$ and $21 v^{2}$ .

$9 + 0 - 49 v^{4}$

Step 2.3

Add $9$ and $0$ .

$9 - 49 v^{4}$