Algebra for Beginners |
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Page 5
... already given , and by combining the terms the numerical value of the whole expres- sion is obtained . 13. We have already , in Art . 8 , drawn attention to the importance of carefully distinguishing between coefficient and index ...
... already given , and by combining the terms the numerical value of the whole expres- sion is obtained . 13. We have already , in Art . 8 , drawn attention to the importance of carefully distinguishing between coefficient and index ...
Page 16
... already come under the head of addition of like terms , of which some are negative . [ Art . 20. ] Thus 5a - 3a = 2α , 3a - 7a = -4a , -3a - 6a9a . Since subtraction is the reverse of addition , + b − b = 0 ; . a = a + b - b . Now ...
... already come under the head of addition of like terms , of which some are negative . [ Art . 20. ] Thus 5a - 3a = 2α , 3a - 7a = -4a , -3a - 6a9a . Since subtraction is the reverse of addition , + b − b = 0 ; . a = a + b - b . Now ...
Page 29
... already 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 ...
... already 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 ...
Page 38
... already been given in Arts . 24 and 25 . When an expression within brackets is preceded by the sign + , the brackets can be removed without making any change in the expression . - When an expression within brackets is preceded by the ...
... already been given in Arts . 24 and 25 . When an expression within brackets is preceded by the sign + , the brackets can be removed without making any change in the expression . - When an expression within brackets is preceded by the ...
Page 45
... already 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 − { xy + 2y3 , x2 - xy - žy2 . x2 + xy - y2 x2 - 3xy + 2y2 x2- xy ...
... already 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 − { xy + 2y3 , x2 - xy - žy2 . x2 + xy - y2 x2 - 3xy + 2y2 x2- xy ...
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Common terms and phrases
A's age a²+b² acres algebraical sum Arithmetic arranged B's age beginner binomial cents CHAPTER coefficient Completing the square compound expressions contains convenient descending powers difference digits dimes Divide division divisor Elementary Algebra equal examples see Elementary EXAMPLES XVII 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 Simplify simultaneous equations Solve the equations square root subtract Transposing trinomial unknown quantities walk whence write yards
Popular passages
Page 160 - An equation which contains the square of the unknown quantity, but no higher power, is called a quadratic equation, or an equation of the second degree. If the equation contains both the square and the first power of the unknown, it is called...
Page 188 - Elementary Trigonometry" etc Edited mi*l Arranged for American Schools By CHARLOTTE ANGAS SCOTT, D.SC., Head of Math. Deft., Bryn Mauir College, Pa. 1 6mo. Cloth. 75 cents. " Evidently the work of a thoroughly good teacher. The elementary truth, that arithmetic is common sense, is the principle which pervades the whole book, and no process, however simple, is deemed unworthy of clear explanation. Where it seems advantageous, a rule is given after the explanation. . . . Mr. Lock's admirable Trigonometry...
Page 105 - 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 - 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 87 - 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 89 - The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first and second, plus the square of the second.