Basic Math Examples

$(u v^{2} - 2 a) (u v^{2} + 2 a)$

Step 1

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

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Step 1.1

Apply the distributive property.

$u v^{2} (u v^{2} + 2 a) - 2 a (u v^{2} + 2 a)$

Step 1.2

Apply the distributive property.

$u v^{2} (u v^{2}) + u v^{2} (2 a) - 2 a (u v^{2} + 2 a)$

Step 1.3

Apply the distributive property.

$u v^{2} (u v^{2}) + u v^{2} (2 a) - 2 a (u v^{2}) - 2 a (2 a)$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $u v^{2} (u v^{2}) + u v^{2} (2 a) - 2 a (u v^{2}) - 2 a (2 a)$ .

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Step 2.1.1

Reorder the factors in the terms $u v^{2} (2 a)$ and $- 2 a (u v^{2})$ .

$u v^{2} (u v^{2}) + 2 v^{2} a u - 2 v^{2} a u - 2 a (2 a)$

Step 2.1.2

Subtract $2 v^{2} a u$ from $2 v^{2} a u$ .

$u v^{2} (u v^{2}) + 0 - 2 a (2 a)$

Step 2.1.3

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

$u v^{2} (u v^{2}) - 2 a (2 a)$

Step 2.2

Simplify each term.

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Step 2.2.1

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

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Step 2.2.1.1

Move $u$ .

$u \cdot u v^{2} v^{2} - 2 a (2 a)$

Step 2.2.1.2

Multiply $u$ by $u$ .

$u^{2} v^{2} v^{2} - 2 a (2 a)$

Step 2.2.2

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

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Step 2.2.2.1

Move $v^{2}$ .

$u^{2} (v^{2} v^{2}) - 2 a (2 a)$

Step 2.2.2.2

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

$u^{2} v^{2 + 2} - 2 a (2 a)$

Step 2.2.2.3

Add $2$ and $2$ .

$u^{2} v^{4} - 2 a (2 a)$

Step 2.2.3

Rewrite using the commutative property of multiplication.

$u^{2} v^{4} - 2 \cdot 2 a \cdot a$

Step 2.2.4

Multiply $a$ by $a$ by adding the exponents.

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Step 2.2.4.1

Move $a$ .

$u^{2} v^{4} - 2 \cdot 2 (a \cdot a)$

Step 2.2.4.2

Multiply $a$ by $a$ .

$u^{2} v^{4} - 2 \cdot 2 a^{2}$

Step 2.2.5

Multiply $- 2$ by $2$ .

$u^{2} v^{4} - 4 a^{2}$