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Chapter 0: Problem 82

Find each product. $$(5 x+1+6 y)^{2}$$

Short Answer

Expert verified
The square of the expression \( (5x + 1 + 6y) \) is \( 25x^2 + 10x + 60xy + 36y^2 + 12y + 1 \)

Step by step solution

01

Identify the elements in the expression

In the expression to be squared, \( (5x + 1 + 6y) \), the elements are \( a = 5x \), \( b = 1 \), and \( c = 6y \)
02

Expand the expression

Using the formula \( (a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc \), substitute the identified elements into the formula. This would result in \( (5x)^2 + 1^2 + (6y)^2 + 2(5x)(1) + 2(5x)(6y) + 2(1)(6y) \)
03

Calculate and simplify

The next step is to perform the operations: \( 25x^2 + 1 + 36y^2 + 10x + 60xy + 12y \), which can be simplified to \( 25x^2 + 10x + 60xy + 36y^2 + 12y + 1 \)

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Most popular questions from this chapter

Explain how to solve \(x^{2}+6 x+8=0\) using factoring and the zero-product principle.

Rationalize the numerator. $$\frac{\sqrt{x}+\sqrt{y}}{x^{2}-y^{2}}$$

What is a rational expression?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. The rational expressions $$\frac{7}{14 x} \text { and } \frac{7}{14+x}$$ can both be simplified by dividing each numerator and each denominator by 7

This will help you prepare for the material covered in the next section. Evaluate $$\frac{-b-\sqrt{b^{2}-4 a c}}{2 a}$$ for \(a=2, b=9,\) and \(c=-5\)
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