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Chapter 0: Problem 74

Find each product. $$(x+y+5)(x+y-5)$$

Short Answer

Expert verified
The product of the binomials \((x+y+5)(x+y-5)\) is \(x^2 + 2xy + y^2 - 25\).

Step by step solution

01

Identify the Form of the Expressions

Recognize that \((x+y+5)(x+y-5)\) is in the form of \((a+b)(a-b)\) where \(a = x+y\) and \(b=5\).
02

Apply Difference of Squares

Apply the formula \(a^2 - b^2\) to the expression. In this case, square \(a = x + y\) to get \((x+y)^2\) and square \(b = 5\) to get \(25\). Doing this provides the new expression \((x+y)^2 - (5)^2\).
03

Simplify the Expression

Expand and simplify \((x+y)^2\) which will yield \(x^2 + 2xy + y^2\). Do the same for \(5^2\) which will yield \(25\). After simplifying the expression becomes \(x^2 + 2xy + y^2 - 25\) .

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