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Chapter 14: Problem 9

Use the Binomial Theorem to expand each binomial and express the result in simplified form. $$(x+2)^{3}$$

Short Answer

Expert verified
\((x + 2)^3 = x^3 + 6x^2 + 12x +8\)

Step by step solution

01

STEP 1: Identify a, b and n

In this exercise, \( a = x \), \( b = 2 \) and \( n = 3 \).
02

STEP 2: Apply the Binomial Theorem

Plug \( a \), \( b \), and \( n \) into the Binomial Theorem.\nSo, \((x + 2)^3 = x^3 + 3* x^{3-1}*2 + 3* x^{3-2}*2^2 + 2^3\).
03

STEP 3: Simplify

\((x + 2)^3 = x^3 + 3*x^2*2 + 3*x*4 + 8\)\nSimplifying further gets us \((x + 2)^3 = x^3 + 6x^2 + 12x +8\)

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Most popular questions from this chapter

Use the formula for the value of an annuity to solve Exercises. Round answers to the nearest dollar. To save money for a sabbatical to earn a master's degree, you deposit \(\$ 2000\) at the end of each year in an annuity that pays \(7.5 \%\) compounded annually. a. How much will you have saved at the end of five years? b. Find the interest.

Use the formula for the sum of the first n terms of a geometric sequence to solve. You save \(\$ 1\) the first day of a month, \(\$ 2\) the second day, \(\$ 4\) the third day, continuing to double your savings each day. What will your total savings be for the first 30 days?

What is an annuity?

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I was able to find the sum of the first fifty terms of an arithmetic sequence even though I did not identify every term.

$$\text { Solve: } \log \left(x^{2}-25\right)-\log (x+5)=3$$
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