Precalculus Examples

$(5 x^{a - b} + y^{b - a}) (x^{b - a} - y^{a - b})$

Step 1

Expand $(5 x^{a - b} + y^{b - a}) (x^{b - a} - y^{a - b})$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$5 x^{a - b} (x^{b - a} - y^{a - b}) + y^{b - a} (x^{b - a} - y^{a - b})$

Step 1.2

Apply the distributive property.

$5 x^{a - b} x^{b - a} + 5 x^{a - b} (- y^{a - b}) + y^{b - a} (x^{b - a} - y^{a - b})$

Step 1.3

Apply the distributive property.

$5 x^{a - b} x^{b - a} + 5 x^{a - b} (- y^{a - b}) + y^{b - a} x^{b - a} + y^{b - a} (- y^{a - b})$

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 $x^{a - b}$ by $x^{b - a}$ by adding the exponents.

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Step 2.1.1.1

Move $x^{b - a}$ .

$5 (x^{b - a} x^{a - b}) + 5 x^{a - b} (- y^{a - b}) + y^{b - a} x^{b - a} + y^{b - a} (- y^{a - b})$

Step 2.1.1.2

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

$5 x^{b - a + a - b} + 5 x^{a - b} (- y^{a - b}) + y^{b - a} x^{b - a} + y^{b - a} (- y^{a - b})$

Step 2.1.1.3

Combine the opposite terms in $b - a + a - b$ .

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Step 2.1.1.3.1

Add $- a$ and $a$ .

$5 x^{b + 0 - b} + 5 x^{a - b} (- y^{a - b}) + y^{b - a} x^{b - a} + y^{b - a} (- y^{a - b})$

Step 2.1.1.3.2

Add $b$ and $0$ .

$5 x^{b - b} + 5 x^{a - b} (- y^{a - b}) + y^{b - a} x^{b - a} + y^{b - a} (- y^{a - b})$

Step 2.1.1.3.3

Subtract $b$ from $b$ .

$5 x^{0} + 5 x^{a - b} (- y^{a - b}) + y^{b - a} x^{b - a} + y^{b - a} (- y^{a - b})$

Step 2.1.2

Simplify $5 x^{0}$ .

$5 + 5 x^{a - b} (- y^{a - b}) + y^{b - a} x^{b - a} + y^{b - a} (- y^{a - b})$

Step 2.1.3

Rewrite using the commutative property of multiplication.

$5 + 5 \cdot - 1 x^{a - b} y^{a - b} + y^{b - a} x^{b - a} + y^{b - a} (- y^{a - b})$

Step 2.1.4

Multiply $5$ by $- 1$ .

$5 - 5 x^{a - b} y^{a - b} + y^{b - a} x^{b - a} + y^{b - a} (- y^{a - b})$

Step 2.1.5

Rewrite using the commutative property of multiplication.

$5 - 5 x^{a - b} y^{a - b} + y^{b - a} x^{b - a} - y^{b - a} y^{a - b}$

Step 2.1.6

Multiply $y^{b - a}$ by $y^{a - b}$ by adding the exponents.

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Step 2.1.6.1

Move $y^{a - b}$ .

$5 - 5 x^{a - b} y^{a - b} + y^{b - a} x^{b - a} - (y^{a - b} y^{b - a})$

Step 2.1.6.2

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

$5 - 5 x^{a - b} y^{a - b} + y^{b - a} x^{b - a} - y^{a - b + b - a}$

Step 2.1.6.3

Combine the opposite terms in $a - b + b - a$ .

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Step 2.1.6.3.1

Add $- b$ and $b$ .

$5 - 5 x^{a - b} y^{a - b} + y^{b - a} x^{b - a} - y^{a + 0 - a}$

Step 2.1.6.3.2

Add $a$ and $0$ .

$5 - 5 x^{a - b} y^{a - b} + y^{b - a} x^{b - a} - y^{a - a}$

Step 2.1.6.3.3

Subtract $a$ from $a$ .

$5 - 5 x^{a - b} y^{a - b} + y^{b - a} x^{b - a} - y^{0}$

Step 2.1.7

Simplify $- y^{0}$ .

$5 - 5 x^{a - b} y^{a - b} + y^{b - a} x^{b - a} - 1$

Step 2.2

Subtract $1$ from $5$ .

$- 5 x^{a - b} y^{a - b} + y^{b - a} x^{b - a} + 4$