/*! 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 46 Expand the expression. $$ (3... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 46

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

Short Answer

Expert verified
The expanded expression is \((3 + \sqrt{2})^2 = 11 + 6\sqrt{2}\).

Step by step solution

01

Identify the values of a and b

In the given expression \((3 + \sqrt{2})^2\), we have \(a = 3\) and \(b = \sqrt{2}\).
02

Apply the binomial formula

Using the binomial formula \((a + b)^2 = a^2 + 2ab + b^2\), substitute the values of a and b from step 1: \((3 + \sqrt{2})^2 = (3)^2 + 2(3)(\sqrt{2}) + (\sqrt{2})^2\)
03

Calculate a^2, 2ab, and b^2

Calculate the individual terms in the expanded expression: \((3)^2 = 9\) \(2(3)(\sqrt{2}) = 6\sqrt{2}\) \((\sqrt{2})^2 = 2\)
04

Combine the terms

Combine the terms from step 3 to find the expanded expression: \((3 + \sqrt{2})^2 = 9 + 6\sqrt{2} + 2\)
05

Simplify the expression

Simplify the expanded expression by adding the constant terms 9 and 2: \((3 + \sqrt{2})^2 = 11 + 6\sqrt{2}\) The expanded expression is \((3 + \sqrt{2})^2 = 11 + 6\sqrt{2}\).

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