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Chapter 5: Problem 75

Find each product. $$(x+y+1)(x+y-1)$$

Short Answer

Expert verified
The product of the binomials \((x+y+1)(x+y-1)\) is \(x^2 + 2xy + y^2 - 1\).

Step by step solution

01

Identify the structure

Recognize the structure of the given expression, \((x+y+1)(x+y-1)\). It resembles a difference of squares pattern, i.e., \((a-b)(a+b)\), where `a` and `b` are the binomial `x+y` and the number `1` respectively.
02

Apply the difference of squares formula

Apply the difference of squares formula, which states \((a+b)(a-b) = a^2 - b^2\). Here, `a` is the binomial \(x+y\) and `b` is `1`. Therefore, when applying the formula, we get \((x+y)^2 - 1^2\).
03

Simplify the expression

First, simplify \((x+y)^2\) to \(x^2 + 2xy + y^2\).Afterwards subtract \(1^2\) which equals `1`, to get the final result of \(x^2 + 2xy + y^2 - 1\).

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