Pre-Algebra Examples

$(7 u + 6 v) (7 u - 6 v)$

Step 1

Expand $(7 u + 6 v) (7 u - 6 v)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$7 u (7 u - 6 v) + 6 v (7 u - 6 v)$

Step 1.2

Apply the distributive property.

$7 u (7 u) + 7 u (- 6 v) + 6 v (7 u - 6 v)$

Step 1.3

Apply the distributive property.

$7 u (7 u) + 7 u (- 6 v) + 6 v (7 u) + 6 v (- 6 v)$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $7 u (7 u) + 7 u (- 6 v) + 6 v (7 u) + 6 v (- 6 v)$ .

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Step 2.1.1

Reorder the factors in the terms $7 u (- 6 v)$ and $6 v (7 u)$ .

$7 u (7 u) - 6 \cdot 7 u v + 6 \cdot 7 u v + 6 v (- 6 v)$

Step 2.1.2

Add $- 6 \cdot 7 u v$ and $6 \cdot 7 u v$ .

$7 u (7 u) + 0 + 6 v (- 6 v)$

Step 2.1.3

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

$7 u (7 u) + 6 v (- 6 v)$

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

$7 \cdot 7 u \cdot u + 6 v (- 6 v)$

Step 2.2.2

Multiply $u$ by $u$ by adding the exponents.

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Step 2.2.2.1

Move $u$ .

$7 \cdot 7 (u \cdot u) + 6 v (- 6 v)$

Step 2.2.2.2

Multiply $u$ by $u$ .

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

Step 2.2.3

Multiply $7$ by $7$ .

$49 u^{2} + 6 v (- 6 v)$

Step 2.2.4

Rewrite using the commutative property of multiplication.

$49 u^{2} + 6 \cdot - 6 v \cdot v$

Step 2.2.5

Multiply $v$ by $v$ by adding the exponents.

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Step 2.2.5.1

Move $v$ .

$49 u^{2} + 6 \cdot - 6 (v \cdot v)$

Step 2.2.5.2

Multiply $v$ by $v$ .

$49 u^{2} + 6 \cdot - 6 v^{2}$

Step 2.2.6

Multiply $6$ by $- 6$ .

$49 u^{2} - 36 v^{2}$