Finite Math Examples

$(x y + a b) (x y - a b)$

Step 1

Expand $(x y + a b) (x y - a b)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$x y (x y - a b) + a b (x y - a b)$

Step 1.2

Apply the distributive property.

$x y (x y) + x y (- a b) + a b (x y - a b)$

Step 1.3

Apply the distributive property.

$x y (x y) + x y (- a b) + a b (x y) + a b (- a b)$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $x y (x y) + x y (- a b) + a b (x y) + a b (- a b)$ .

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Step 2.1.1

Reorder the factors in the terms $x y (- a b)$ and $a b (x y)$ .

$x y (x y) - a b x y + a b x y + a b (- a b)$

Step 2.1.2

Add $- a b x y$ and $a b x y$ .

$x y (x y) + 0 + a b (- a b)$

Step 2.1.3

Add $x y (x y)$ and $0$ .

$x y (x y) + a b (- a b)$

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $x$ by $x$ by adding the exponents.

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Step 2.2.1.1

Move $x$ .

$x \cdot x y \cdot y + a b (- a b)$

Step 2.2.1.2

Multiply $x$ by $x$ .

$x^{2} y \cdot y + a b (- a b)$

Step 2.2.2

Multiply $y$ by $y$ by adding the exponents.

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Step 2.2.2.1

Move $y$ .

$x^{2} (y \cdot y) + a b (- a b)$

Step 2.2.2.2

Multiply $y$ by $y$ .

$x^{2} y^{2} + a b (- a b)$

Step 2.2.3

Rewrite using the commutative property of multiplication.

$x^{2} y^{2} - a b (a b)$

Step 2.2.4

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

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Step 2.2.4.1

Move $a$ .

$x^{2} y^{2} - (a \cdot a) b \cdot b$

Step 2.2.4.2

Multiply $a$ by $a$ .

$x^{2} y^{2} - a^{2} b \cdot b$

Step 2.2.5

Multiply $b$ by $b$ by adding the exponents.

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Step 2.2.5.1

Move $b$ .

$x^{2} y^{2} - a^{2} (b \cdot b)$

Step 2.2.5.2

Multiply $b$ by $b$ .

$x^{2} y^{2} - a^{2} b^{2}$