## A Complete Course in AlgebraLeach, Shewell, and Sanborn, 1885 |

### From inside the book

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**following**, the negative quantities being interpreted as explained in Art . 44 . 1. If a man owes $ 5 , and incurs a ...**rule**of Art . 53 . The sum of 2a , 3a , and 6a is 11 a . The sum of - a and 12 a is - 13 α . Hence , the required sum is ... Page 18

... following : 20. 5 ax , -116 , 21. 2a , 5b , - 3c , 22. 5m , - 2n2 , n , 23. 3x , y , — ax , and 6b . - 8b , and 9c ...

... following : 20. 5 ax , -116 , 21. 2a , 5b , - 3c , 22. 5m , - 2n2 , n , 23. 3x , y , — ax , and 6b . - 8b , and 9c ...

**following rule**: 3a - 2x + 3y - mn , Ans . 12. 2x3 - 52 - x + 7 , 3x2 18 ALGEBRA . Addition of Polynomials. Page 19

Webster Wells. From the above principles we derive the

Webster Wells. From the above principles we derive the

**following rule**: To add two or more expressions , set them down one under- neath the other , similar terms being in the same vertical column . Find the sum of the terms in each ... Page 24

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**following rule**for removing a paren- thesis : A parenthesis preceded by a + sign may be removed without altering the signs of the enclosed terms . A parenthesis preceded by a sign may be removed , if the sign of each enclosed term be ... Page 25

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**rule**of Art . 67 , the expression becomes 2a - 3b - 5a + 4b + 4 a − b = a , Ans . Parentheses are often found enclosing others . In this case they may be removed in succession by the**rule**...**following**expressions to their simplest ...### Other editions - View all

### Common terms and phrases

a²-b² a²+2ab+b² a²b a²b² ab² ab³ Adding Algebra arithmetical means arithmetical progression ax² binomial cents change the sign coefficient cologarithm Completing the square cube root decimal derive the formula digits dividend divisor EXAMPLES exponent expression Extracting the square Find the H.C.F. Find the value Find two numbers following equations following rule geometrical progression Hence highest common factor last term less logarithm lowest common multiple mantissa minuend monomial Note number of terms parenthesis perfect square polynomial positive proportion QUADRATIC EQUATIONS quotient radical sign Reduce the following remainder Required the number result rods rule of Art second term simplest form Solve the equation Solve the following square root subtract third Transposing trial-divisor twice unknown quantity Whence x²y xy² α² α³ ах у² ху

### Popular passages

Page 166 - Arts. 200 and 201 we derive the following rule : Extract the required root of the numerical coefficient, and divide the exponent of each letter by the index of the root.

Page 213 - In any trinomial square (Art. 108), the middle term is twice the product of the square roots of the first and third terms...

Page 44 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.

Page 49 - The exponent of b in the second term is 1, and increases by 1 in each succeeding term.

Page 255 - The first and fourth terms of a proportion are called the extremes; and the second and third terms the means. Thus, in the proportion a : b = с : d, a and d are the extremes, and b and с the means.

Page 258 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: b = c: d = e:f.

Page 5 - If equal quantities be divided by the same quantity, or equal quantities, the quotients will be equal. 5. If the same quantity be both added to and subtracted from another, the value of the latter will not be changed.

Page 44 - 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 107 - Any term may be transposed from one side of an equation to the other by changing its sign. For, consider the equation x + a = b.

Page 227 - A' courier proceeds from P to Q in 14 hours. A second courier starts at the same time from a place 10 miles behind P, and arrives at Q at the same time as the first courier. The second courier finds that he takes half an hour less than the first to accomplish 20 miles. Find the distance from P to Q.