Algebra for Beginners |
From inside the book
Results 1-5 of 12
Page 29
... explained , it is of the utmost importance that the student should soon learn to write down the product rapidly by inspection . This is done by observing in what way the coefficients of the terms in the product arise , and noticing that ...
... explained , it is of the utmost importance that the student should soon learn to write down the product rapidly by inspection . This is done by observing in what way the coefficients of the terms in the product arise , and noticing that ...
Page 32
... explained in the Theory of Indices . [ See Elementary Algebra , Chap . xxxI . ] Rule . To divide a compound expression by a single factor , divide each term separately by that factor , and take the algebraic sum of the partial quotients ...
... explained in the Theory of Indices . [ See Elementary Algebra , Chap . xxxI . ] Rule . To divide a compound expression by a single factor , divide each term separately by that factor , and take the algebraic sum of the partial quotients ...
Page 33
... 6 ) x2 + 11x + 30 ( x x2 + 6x 5 + 30 On repeating the process above explained , we find that the next term in the quotient is +5 . H.A. The entire operation is more compactly written as follows : VI . ] 333 DIVISION .
... 6 ) x2 + 11x + 30 ( x x2 + 6x 5 + 30 On repeating the process above explained , we find that the next term in the quotient is +5 . H.A. The entire operation is more compactly written as follows : VI . ] 333 DIVISION .
Page 45
... explained in the case of integral coefficients are still applicable when the coefficients are fractional . Example 1. Find the sum of 3x2 + xy - y2 , - x2 - 3xy + 2y2 , 3x2 - xy - žy2 . x2 + xy - y2 x2 - 3xy + 2y2 x2- xy - by2 x2 - 4 xy ...
... explained in the case of integral coefficients are still applicable when the coefficients are fractional . Example 1. Find the sum of 3x2 + xy - y2 , - x2 - 3xy + 2y2 , 3x2 - xy - žy2 . x2 + xy - y2 x2 - 3xy + 2y2 x2- xy - by2 x2 - 4 xy ...
Page 95
... explained in the next article , which is quite general , and applicable to all cases . But the student is advised , here and elsewhere , to employ methods of inspection in preference to rules . To Find the Square Root of a Compound ...
... explained in the next article , which is quite general , and applicable to all cases . But the student is advised , here and elsewhere , to employ methods of inspection in preference to rules . To Find the Square Root of a Compound ...
Common terms and phrases
a²+b² acres algebraical sum Arithmetic arranged beginner cents CHAPTER coefficient Completing the square compound expressions convenient cube root descending powers difference digits dimes Divide division divisor Elementary Algebra equal examples see Elementary EXAMPLES XVII exceeds Find the highest Find the lowest find the number Find the product Find the square Find the sum find the value following expressions given expressions half-dollars Hence highest common factor lowest common denominator lowest common multiple lowest terms miles an hour miles per hour minute-hand Multiply negative numerator and denominator obtain quadratic equation quotient Reduce to lowest remainder removing brackets Resolve into factors result rule of signs side simple equation simultaneous equations Solve the equations square root Subtract Transposing trinomial unknown quantities walk whence write yards α α
Popular passages
Page 91 - The product is a2+2a6-}-62; from which it appears, that 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 - Conversely, the difference of the squares of any two quantities is equal to the product of the sum and the difference of the two quantities.
Page 89 - It is evident from the Rule of Signs that (1) no even power of any quantity can be negative; (2) any odd power of a quantity will have the same sign as the quantity itself. NOTE. It is especially worthy of notice that the square of every expression, whether positive or negative, is positive.
Page 54 - Transpose all the terms containing the unknown quantity to one side of the equation, and the "known quantities to the other.