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**Extra resources for Algebra & Trigonometry, Edition: 3rd**

**Example text**

Round the number of citizens to the nearest thousand. 75. S. Debt. If the debt is distributed evenly to all citizens, what is the national debt per citizen? Round your answer to the nearest dollar. 76. S. Debt. If the debt is distributed evenly to all citizens, what is the national debt per citizen? Round your answer to the nearest cent. 1 Real Numbers ■ 17 C AT C H T H E M I S TA K E In Exercises 77–80, explain the mistake that is made. 79. Simplify the expression 3(x ϩ 5) Ϫ 2(4 ϩ y). 77. 2749 to two decimal places.

Solution: ᭤ ᭤ ᭤ 5x2(3x5 - x3 + 7x - 4) ᭤ Use the distributive property. ϭ 5x2(3x5) Ϫ 5x2(x3) ϩ 5x2(7x) Ϫ 5x2(4) Multiply each set of monomials. ■ Answer: 12x4 Ϫ 6x3 ϩ 3x2 ■ YO U R T U R N ϭ 15x7 Ϫ 5x5 ϩ 35x3 Ϫ 20x2 Find the product and simplify 3x2(4x2 Ϫ 2x ϩ 1). How do we multiply two polynomials if neither one is a monomial? For example, how do we ﬁnd the product of a binomial and a trinomial such as (2x Ϫ 5)(x2 Ϫ 2x ϩ 3)? Notice that the binomial is a combination of two monomials. Therefore, we treat each monomial, 2x and Ϫ5, separately and then combine our results.

Write the answer in scientiﬁc notation. b. The circumference of the Earth (measured at the equator) is approximately 25,000 miles. If the cell phones in part (a) were to be wrapped around the Earth at the equator, would they circle the Earth completely? If so, approximately how many times? 68. Cell Phones Reaching the Moon. a. If all of the cell phones currently in use were to be lined up next to each other tip to tip, how many miles would the line of cell phones span? Write the answer in scientiﬁc notation.