## Eaton's Elementary Algebra, Designed for the Use of High Schools and AcademiesThompson, Brown, and Company, 1875 |

### From inside the book

Results 6-10 of 16

Page 133

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**binomial**) begins in the first term of the power with an ex- ponent equal to the index of the power , and its exponent decreases regularly by one in each successive term till it dis- appears ; the following quantity ( i . e . the second ... Page 134

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**binomial**are positive , all the terms of the power are positive ; but when the second term is negative , those terms which contain odd powers of the following quantity are negative , and all the others positive ; or every alternate term ... Page 135

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**binomial**have coefficients or exponents other than 1 , the theorem can be made to apply by treating each term as a ...**binomial**by the**binomial**theorem , the work should be completed by the expansion of the enclosed factors ... Page 136

... 14. Expand ( x + 1 ) . 15. Expand ( 1–3 ) . 5 16. Expand ( 2 a2 — 1 ) . - 17. Expand ( +1 ) . 18. Expand ( 1 ) 8 x3 y + x2 y2 + 4 x y + x . 131. The

... 14. Expand ( x + 1 ) . 15. Expand ( 1–3 ) . 5 16. Expand ( 2 a2 — 1 ) . - 17. Expand ( +1 ) . 18. Expand ( 1 ) 8 x3 y + x2 y2 + 4 x y + x . 131. The

**Binomial**Theorem can be applied to the ex- 136 ELEMENTARY ALGEBRA . Page 137

William Frothingham Bradbury. 131. The

William Frothingham Bradbury. 131. The

**Binomial**Theorem can be applied to the ex- pansion of a polynomial . Thus , in ab . - y can C , a + b can be treated as a single term , and the quantity can be written ( a + b ) - C. In like manner ...### Other editions - View all

### Common terms and phrases

2ab+b² a b c a²x² added Algebra arithmetical mean arithmetical progression binomial cents coefficient cologarithm common difference completing the square cube root Divide dividend division dollars elimination equal examples Expand exponent extracting the square fifth figures Find the cube Find the factors Find the fourth Find the greatest Find the least Find the square Find the sum Find the value Find two numbers geometrical progression greatest common divisor Hence horse improper fraction integral quantity least common multiple less logarithm mantissa minus monomial Multiply negative NOTE number of terms obtain OPERATION polynomial proportion quadratic equation quan quotient radical sign ratio reduced gives remainder second term square root Substituting this value subtracted Theorem third tities Transposing trial divisor twice unknown quantity x² y²

### Popular passages

Page 207 - An INVERSE, or RECIPROCAL RATIO, of any two quantities is the ratio of their reciprocals. Thus, the direct ratio of a to b is a : b...

Page 10 - In reducing the equation so as to find the value of the unknown quantities. EXAMPLES FOR PRACTICE. 1. The sum of the ages of a father and his son is 60 years, and the age of the father is double that of the son ; what is the age of each...

Page 44 - ... the square of the second. In the second case, we have (a — &)2 = a2 — 2 ab + b2. (2) That is, the square of the difference of two quantities is equal to the square of the first, minus twice the product of the two, plus the square of the second.

Page 83 - ... quantity. 4. If one member is divided by any quantity, the other member must be divided by an equal quantity. 5. If one member is involved or evolved, the other must be involved or evolved to the same degree. TRANSPOSITION. 100. TRANSPOSITION is the changing of terms from one member of an equation to the other, without destroying the equality.

Page 155 - Resolve the quantity under the radical sign into two factors, one of which is the greatest perfect power of the same degree as the radical.

Page 45 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — b) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.

Page 207 - PROPORTION when the ratio of the first to the second is equal to the ratio of the second to the third.

Page 87 - Four quantities are proportional when the ratio of the first to the second is equal to the ratio of the third to the fourth.

Page 43 - I. The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first by the second, plus the square of the second.

Page 251 - How far from Boston did they meet ? Ans. 42 miles. 163. The product of two numbers is 90 ; and the difference of their cubes is to the cube of their difference as 13 : 3. What are the numbers? 164. A and B start together from the same place and travel in the same direction. A travels the first day 25 kilometers, the second 22, and so on, travelling each day 3 kilometers less than on the preceding day, while B travels 14£ kilometers each day. In what time will the two be together again ? Ans. 8 days.