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Chapter 0: Problem 79

Find each product. $$(x+y+1)^{2}$$

Short Answer

Expert verified
The solution is \(x^2+y^2+2xy+2x+2y+1\)

Step by step solution

01

Understand and Apply the Correct Formula

Recognize that the term provided, \((x+y+1)^{2}\), is a trinomial expression being squared. The formula for squaring a trinomial expression \((a+b+c)^2\) is \(a^2+b^2+c^2+2ab+2bc+2ca\). In this exercise, \(a=x\), \(b=y\), and \(c=1\).
02

Substitute and Solve

Now substitute: \(a^2+b^2+c^2+2ab+2bc+2ca\) can be rewritten as \(x^2+y^2+1^2+2xy+2y*1+2*1*x\). After simplifying, we get \(x^2+y^2+1+2xy+2y+2x\). This can finally be rewritten by grouping like terms to \(x^2+y^2+2xy+2x+2y+1\).

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Most popular questions from this chapter

What is a quadratic equation?

Perform the indicated operations. Simplify the result, if possible. $$\frac{y^{-1}-(y+2)^{-1}}{2}$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When performing the division $$\frac{7 x}{x+3}+\frac{(x+3)^{2}}{x-5}$$ I began by dividing the numerator and the denominator by the common factor, \(x+3\).

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{2 x-1}{x-7}+\frac{3 x-1}{x-7}-\frac{5 x-2}{x-7}=0$$

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. A company manufactures and sells blank audiocassette tapes. The weekly fixed cost is \(\$ 10,000\) and it costs \(\$ 0.40\) to produce each tape. The selling price is \(\$ 2.00\) per tape. How many tapes must be produced and sold each week for the company to generate a profit?
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