Algebra for Beginners |
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Page 4
... contains a zero factor . Therefore ab3xy2 = 0 when x = 0 , whatever be the values of a , b , y . Again , if c = 0 , then c3 = 0 ; therefore ab2c3 = 0 , whatever values a and b may have . Note . Every power of 0 is 0 . EXAMPLES I. b . If ...
... contains a zero factor . Therefore ab3xy2 = 0 when x = 0 , whatever be the values of a , b , y . Again , if c = 0 , then c3 = 0 ; therefore ab2c3 = 0 , whatever values a and b may have . Note . Every power of 0 is 0 . EXAMPLES I. b . If ...
Page 5
... contain more than one term . In these each term can be dealt with singly by the rules 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 ...
... contain more than one term . In these each term can be dealt with singly by the rules 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 ...
Page 6
... contains a zero factor is itself zero , and may be called a zero term . Example . If a = 2 , b = 0 , x = 5 , y = 3 , find the value of 5a3- ab2 + 2x2y + 3bxy . The expression = ( 5 × 23 ) − 0 + ( 2 × 52 × 3 ) +0 = 40 + 150 = 190 . Note ...
... contains a zero factor is itself zero , and may be called a zero term . Example . If a = 2 , b = 0 , x = 5 , y = 3 , find the value of 5a3- ab2 + 2x2y + 3bxy . The expression = ( 5 × 23 ) − 0 + ( 2 × 52 × 3 ) +0 = 40 + 150 = 190 . Note ...
Page 15
... contains powers of two letters , and is arranged according to descend- ing powers of b , and ascending powers of a . EXAMPLES III . b . Find the sum of the following expressions : 1. x2 + 3xy - 3y2 ; -3x2 + xy + 2y2 ; 2x2 - 3xy + y2 . 2 ...
... contains powers of two letters , and is arranged according to descend- ing powers of b , and ascending powers of a . EXAMPLES III . b . Find the sum of the following expressions : 1. x2 + 3xy - 3y2 ; -3x2 + xy + 2y2 ; 2x2 - 3xy + y2 . 2 ...
Page 17
... containing different powers of the same letter being unlike must stand in different columns . -2-3 3x2 - 2x +1 - x3 - 3x2 + 2x + 1 In the first and last columns , as there is nothing to be subtracted , the terms are put down without ...
... containing different powers of the same letter being unlike must stand in different columns . -2-3 3x2 - 2x +1 - x3 - 3x2 + 2x + 1 In the first and last columns , as there is nothing to be subtracted , the terms are put down without ...
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.