Finite Math Examples

$(x^{\frac{1}{4}} + y^{\frac{1}{4}}) (x^{\frac{1}{4}} - y^{\frac{1}{4}})$

Step 1

Expand $(x^{\frac{1}{4}} + y^{\frac{1}{4}}) (x^{\frac{1}{4}} - y^{\frac{1}{4}})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$x^{\frac{1}{4}} (x^{\frac{1}{4}} - y^{\frac{1}{4}}) + y^{\frac{1}{4}} (x^{\frac{1}{4}} - y^{\frac{1}{4}})$

Step 1.2

Apply the distributive property.

$x^{\frac{1}{4}} x^{\frac{1}{4}} + x^{\frac{1}{4}} (- y^{\frac{1}{4}}) + y^{\frac{1}{4}} (x^{\frac{1}{4}} - y^{\frac{1}{4}})$

Step 1.3

Apply the distributive property.

$x^{\frac{1}{4}} x^{\frac{1}{4}} + x^{\frac{1}{4}} (- y^{\frac{1}{4}}) + y^{\frac{1}{4}} x^{\frac{1}{4}} + y^{\frac{1}{4}} (- y^{\frac{1}{4}})$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $x^{\frac{1}{4}} x^{\frac{1}{4}} + x^{\frac{1}{4}} (- y^{\frac{1}{4}}) + y^{\frac{1}{4}} x^{\frac{1}{4}} + y^{\frac{1}{4}} (- y^{\frac{1}{4}})$ .

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Step 2.1.1

Reorder the factors in the terms $x^{\frac{1}{4}} (- y^{\frac{1}{4}})$ and $y^{\frac{1}{4}} x^{\frac{1}{4}}$ .

$x^{\frac{1}{4}} x^{\frac{1}{4}} - x^{\frac{1}{4}} y^{\frac{1}{4}} + x^{\frac{1}{4}} y^{\frac{1}{4}} + y^{\frac{1}{4}} (- y^{\frac{1}{4}})$

Step 2.1.2

Add $- x^{\frac{1}{4}} y^{\frac{1}{4}}$ and $x^{\frac{1}{4}} y^{\frac{1}{4}}$ .

$x^{\frac{1}{4}} x^{\frac{1}{4}} + 0 + y^{\frac{1}{4}} (- y^{\frac{1}{4}})$

Step 2.1.3

Add $x^{\frac{1}{4}} x^{\frac{1}{4}}$ and $0$ .

$x^{\frac{1}{4}} x^{\frac{1}{4}} + y^{\frac{1}{4}} (- y^{\frac{1}{4}})$

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $x^{\frac{1}{4}}$ by $x^{\frac{1}{4}}$ by adding the exponents.

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Step 2.2.1.1

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

$x^{\frac{1}{4} + \frac{1}{4}} + y^{\frac{1}{4}} (- y^{\frac{1}{4}})$

Step 2.2.1.2

Combine the numerators over the common denominator.

$x^{\frac{1 + 1}{4}} + y^{\frac{1}{4}} (- y^{\frac{1}{4}})$

Step 2.2.1.3

Add $1$ and $1$ .

$x^{\frac{2}{4}} + y^{\frac{1}{4}} (- y^{\frac{1}{4}})$

Step 2.2.1.4

Cancel the common factor of $2$ and $4$ .

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Step 2.2.1.4.1

Factor $2$ out of $2$ .

$x^{\frac{2 (1)}{4}} + y^{\frac{1}{4}} (- y^{\frac{1}{4}})$

Step 2.2.1.4.2

Cancel the common factors.

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Step 2.2.1.4.2.1

Factor $2$ out of $4$ .

$x^{\frac{2 \cdot 1}{2 \cdot 2}} + y^{\frac{1}{4}} (- y^{\frac{1}{4}})$

Step 2.2.1.4.2.2

Cancel the common factor.

$x^{\frac{2 \cdot 1}{2 \cdot 2}} + y^{\frac{1}{4}} (- y^{\frac{1}{4}})$

Step 2.2.1.4.2.3

Rewrite the expression.

$x^{\frac{1}{2}} + y^{\frac{1}{4}} (- y^{\frac{1}{4}})$

Step 2.2.2

Rewrite using the commutative property of multiplication.

$x^{\frac{1}{2}} - y^{\frac{1}{4}} y^{\frac{1}{4}}$

Step 2.2.3

Multiply $y^{\frac{1}{4}}$ by $y^{\frac{1}{4}}$ by adding the exponents.

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Step 2.2.3.1

Move $y^{\frac{1}{4}}$ .

$x^{\frac{1}{2}} - (y^{\frac{1}{4}} y^{\frac{1}{4}})$

Step 2.2.3.2

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

$x^{\frac{1}{2}} - y^{\frac{1}{4} + \frac{1}{4}}$

Step 2.2.3.3

Combine the numerators over the common denominator.

$x^{\frac{1}{2}} - y^{\frac{1 + 1}{4}}$

Step 2.2.3.4

Add $1$ and $1$ .

$x^{\frac{1}{2}} - y^{\frac{2}{4}}$

Step 2.2.3.5

Cancel the common factor of $2$ and $4$ .

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Step 2.2.3.5.1

Factor $2$ out of $2$ .

$x^{\frac{1}{2}} - y^{\frac{2 (1)}{4}}$

Step 2.2.3.5.2

Cancel the common factors.

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Step 2.2.3.5.2.1

Factor $2$ out of $4$ .

$x^{\frac{1}{2}} - y^{\frac{2 \cdot 1}{2 \cdot 2}}$

Step 2.2.3.5.2.2

Cancel the common factor.

$x^{\frac{1}{2}} - y^{\frac{2 \cdot 1}{2 \cdot 2}}$

Step 2.2.3.5.2.3

Rewrite the expression.

$x^{\frac{1}{2}} - y^{\frac{1}{2}}$