/*! 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 55 Expand the expression. $$ (1... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 55

Expand the expression. $$ (1+2 \sqrt{3 x})^{2} $$

Short Answer

Expert verified
The expanded expression is \( (1 + 2\sqrt{3x})^2 = 1 + 4\sqrt{3x} + 12x \).

Step by step solution

01

Identify a and b

In this case, we have \(a = 1\) and \(b = 2\sqrt{3x}\).
02

Apply the binomial formula

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

Simplify each term

Now, we will simplify each term in the expression: \(1^2 = 1\) \(2(1)(2\sqrt{3x}) = 4\sqrt{3x}\) \((2\sqrt{3x})^2 = 2^2 \times (3x) = 4(3x) = 12x\)
04

Combine the simplified terms

Finally, we add the simplified terms together: \((1 + 2\sqrt{3x})^2 = 1 + 4\sqrt{3x} + 12x\) So, the expanded expression is: \((1 + 2\sqrt{3x})^2 = 1 + 4\sqrt{3x} + 12x\)

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Suppose you start driving a car on a chilly fall day. As you drive, the heater in the car makes the temperature inside the car \(F(t)\) degrees Fahrenheit at time \(t\) minutes after you started driving, where $$ F(t)=40+\frac{30 t^{3}}{t^{3}+100} $$ (a) What was the temperature in the car when you started driving? (b) the car ten minutes after you started driving? (c) What will be the approximate temperature in the car after you have been driving for a long time?

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