Algebra Examples

$(x + y) (x - y)$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$a x^{2} + b x + c$

Step 2

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

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Step 2.1

Apply the distributive property.

$x (x - y) + y (x - y)$

Step 2.2

Apply the distributive property.

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

Step 2.3

Apply the distributive property.

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

Step 3

Simplify terms.

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Step 3.1

Combine the opposite terms in $x \cdot x + x (- y) + y x + y (- y)$ .

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Step 3.1.1

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

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

Step 3.1.2

Add $- x y$ and $x y$ .

$x \cdot x + 0 + y (- y)$

Step 3.1.3

Add $x \cdot x$ and $0$ .

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

Step 3.2

Simplify each term.

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Step 3.2.1

Multiply $x$ by $x$ .

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

Step 3.2.2

Rewrite using the commutative property of multiplication.

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

Step 3.2.3

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

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Step 3.2.3.1

Move $y$ .

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

Step 3.2.3.2

Multiply $y$ by $y$ .

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