/*! 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 45 Expand the expression. $$ (2... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 45

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

Short Answer

Expert verified
The expanded expression is \((2 + \sqrt{3})^2 = 7 + 4\sqrt{3}\).

Step by step solution

01

Write down the formula for binomial expansion

Using the binomial expansion formula \((a + b)^2 = a^2 + 2ab + b^2\), we will substitute \(a = 2\) and \(b = \sqrt{3}\) to find the expanded expression.
02

Substitute the values of a and b into the formula

Replace \(a\) with \(2\) and \(b\) with \(\sqrt{3}\) in the expansion formula: \((2 + \sqrt{3})^2 = (2)^2 + 2(2)(\sqrt{3}) + (\sqrt{3})^2\)
03

Simplify the terms

Calculate the square of each term and simplify: \((2)^2 = 4\) \(2(2)(\sqrt{3}) = 4\sqrt{3}\) \((\sqrt{3})^2 = 3\)
04

Combine the simplified terms

Now, combine the simplified terms: \((2 + \sqrt{3})^2 = 4 + 4\sqrt{3} + 3\)
05

Simplify the expression

Combine the like terms: \((2 + \sqrt{3})^2 = 7 + 4\sqrt{3}\) The expanded expression is \((2 + \sqrt{3})^2 = 7 + 4\sqrt{3}\).

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