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Chapter 0: Problem 73

Find each product. $$(x+y+3)(x+y-3)$$

Short Answer

Expert verified
The product of the binomials \( (x+y+3) \) and \( (x+y-3) \) is \( x^2 +2xy + y^2 - 9 \).

Step by step solution

01

Recognize the Difference of Squares Pattern

The provided expressions \( (x + y + 3) \) and \( (x + y - 3) \) are in a binomial pattern where one has a positive term and the other has its negative counterpart. In other words, they are in a 'difference of squares' pattern.
02

Apply the Formula

Apply the difference of squares formula. In this case, substitute \( a \) for \( x + y \) and \( b \) for 3, into the formula \( a^2 - b^2 \). This gives, \( (x + y)^2 - 3^2 \).
03

Expand the Formula

Expand the formula to obtain the result. The expansion results to \(x^2 +2xy + y^2 - 9 \).

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Most popular questions from this chapter

Will help you prepare for the material covered in the next section. Jane's salary exceeds Jim's by \(\$ 150\) per week. If \(x\) represents Jim's weekly salary, write an algebraic expression that models Jane's weekly salary.

Explain how to simplify a rational expression.

Perform the indicated operations. $$\left(1-\frac{1}{x}\right)\left(1-\frac{1}{x+1}\right)\left(1-\frac{1}{x+2}\right)\left(1-\frac{1}{x+3}\right)$$

How is the quadratic formula derived?

In Exercises \(133-136\), determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{\sqrt{20}}{8}=\frac{\sqrt{10}}{4}$$
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