Expansion of (x - y)(x + y)

MathematicsAlgebraic IdentitiesEasy

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e. $(x - y) \cdot (x + y) = $ $x^2 + xy - xy - y^2$

This question includes visual content: The image shows a handwritten math problem on grid paper. It includes the expression (x - y) . (x + y) = with curved lines indicating the distribution (FOIL method) of the terms. Below that, the expansion x^2 + xy - xy - y^2 is written with further markings beneath.

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Step 1

Hi Selen, let's solve this algebraic expansion together.

Algebraic Expansion

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Step 2

We are given the product of two binomials: x minus y and x plus y.

$$(x - y)(x + y)$$
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Step 3

To solve this, we will use the distributive property, often called the FOIL method, where we multiply every term in the first parenthesis by every term in the second.


Step-by-Step Multiplication

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Step 4

First, we multiply x times x, which gives us x squared.

$$x \cdot x = x^2$$
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Step 5

Next, we multiply the outer terms: x times positive y is plus xy.

$$x \cdot y = +xy$$
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Step 6

Then, the inner terms: negative y times x gives us minus xy.

$$-y \cdot x = -xy$$

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About This Question

Subject
Mathematics
Topic
Algebraic Identities
Difficulty
Easy
Question Type
Open Ended

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