/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 56 Expand the expression. $$ (3... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 56

Expand the expression. $$ (3+2 \sqrt{5 x})^{2} $$

Short Answer

Expert verified
The short answer based on the provided solution is: \((3 + 2\sqrt{5x})^2 = 9 + 12\sqrt{5x} + 20x\)

Step by step solution

01

Identify a and b in the given expression

Let's rewrite the expression so that it fits the \((a+b)^2 = a^2 + 2ab + b^2\) formula. We identify \(a = 3\) and \(b = 2\sqrt{5x}\) from the expression \((3+2\sqrt{5x})^2\).
02

Square a and b

We now square both terms, i.e., we calculate \(a^2\) and \(b^2\). \(a^2 = (3)^2 = 9\) \(b^2 = (2\sqrt{5x})^2 = (2 \cdot 2)(\sqrt{5x} \cdot \sqrt{5x}) = 4 \cdot 5x = 20x\)
03

Find 2ab

Next, we will calculate the term \(2ab\): \(2ab = 2 \cdot 3 \cdot 2\sqrt{5x} = 12\sqrt{5x}\)
04

Add all terms to expand the expression

Finally, we add all the terms from steps 2 and 3 to get the expanded form of the expression: \((3 + 2\sqrt{5x})^2 = a^2 + 2ab + b^2 = 9 + 12\sqrt{5x} + 20x\)

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Most popular questions from this chapter

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