%C3%97(x-y)-answer.jpeg "(x+y)×(x-y) Answer")
Understanding (x+y)×(x-y)
The expression (x+y)×(x-y) is a common algebraic equation that can be simplified using the distributive property or by recognizing a specific pattern.
The Distributive Property Approach
The distributive property states that multiplying a sum by a number is the same as multiplying each addend by that number and then adding the products.
Applying this to our expression:
(x+y)×(x-y) = x(x-y) + y(x-y)
Now, distribute the x and y:
= x² - xy + xy - y²
Notice that the -xy and +xy terms cancel each other out.
Therefore, the simplified expression is:
x² - y²
Recognizing the Pattern
The expression (x+y)×(x-y) represents a common algebraic pattern known as the difference of squares.
Difference of squares states that the product of the sum and difference of two terms is equal to the difference of their squares.
In our case, the two terms are x and y:
(x+y)×(x-y) = x² - y²
Summary
The expression (x+y)×(x-y) can be simplified to x² - y² using the distributive property or by recognizing the difference of squares pattern. This simplified expression is valuable in various algebraic manipulations and problem-solving situations.