/*! 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 48 Expand the expression. $$ (3... [FREE SOLUTION] | 91影视

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Chapter 2: Problem 48

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

Short Answer

Expert verified
The expanded expression is \((3 - 5\sqrt{2})^{2} = 59 - 30\sqrt{2}\).

Step by step solution

01

Identify a and b

In our given expression \((3 - 5\sqrt{2})^{2}\), we can see that \(a = 3\) and \(b = 5\sqrt{2}\).
02

Apply the Binomial Square Formula

Now that we have identified the values for a and b, we can apply the binomial square formula: \((a - b)^{2} = a^{2} - 2ab + b^{2}\).
03

Calculate the Squares of a and b

First, calculate the squares of a and b separately: \(a^{2} = (3)^{2} = 9\) \(b^{2} = (5\sqrt{2})^{2} = (5)^{2}(\sqrt{2})^{2} = 25 \cdot 2 = 50\)
04

Calculate the Middle Term

Now, calculate the middle term, which is 2 times the product of a and b: \(2ab = 2 \cdot 3 \cdot 5\sqrt{2} = 30\sqrt{2}\)
05

Combine the Terms

Finally, combine the calculated terms from steps 3 and 4: \((3 - 5\sqrt{2})^{2} = a^{2} - 2ab + b^{2} = 9 - 30\sqrt{2} + 50\)
06

Simplify the Expression

Combine the integers to simplify the expression: \(9 + 50 = 59\) So, \((3 - 5\sqrt{2})^{2} = 59 - 30\sqrt{2}\)

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Most popular questions from this chapter

Suppose \(p(x)=3 x^{7}-5 x^{3}+7 x-2\) (a) Show that if \(m\) is a zero of \(p\), then $$ \frac{2}{m}=3 m^{6}-5 m^{2}+7 $$ (b) Show that the only possible integer zeros of \(p\) are \(-2,-1,1,\) and 2 . (c) Show that no integer is a zero of \(p\).

Suppose \(p(x)=2 x^{5}+5 x^{4}+2 x^{3}-1 .\) Show that -1 is the only integer zero of \(p\).

Write each expression as the sum of a polynomial and a rational function whose numerator has smaller degree than its denominator. $$ \frac{2 x+1}{x-3} $$

Suppose $$r(x)=\frac{x+1}{x^{2}+3} \quad \text { and } \quad s(x)=\frac{x+2}{x^{2}+5}$$ Find two distinct numbers \(x\) such that \(s(x)=\frac{1}{8}\).

Find all real numbers \(x\) such that $$ x^{6}-8 x^{3}+15=0 $$.
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