Algebra for Beginners |
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Page 2
... convenient to consider any factor , or factors , of a product as the coefficient of the remaining factors . Thus in the product 6ube , 6a may be appropriately called the coefficient of bc . A coefficient which is not merely numerical is ...
... convenient to consider any factor , or factors , of a product as the coefficient of the remaining factors . Thus in the product 6ube , 6a may be appropriately called the coefficient of bc . A coefficient which is not merely numerical is ...
Page 9
... convenient . This process is called collecting terms . -- 21. When quantities are connected by the signs + and the resulting expression is called their algebraical sum . Thus 11a - 27a + 13a = 3a states that the algebraical sum of 11a ...
... convenient . This process is called collecting terms . -- 21. When quantities are connected by the signs + and the resulting expression is called their algebraical sum . Thus 11a - 27a + 13a = 3a states that the algebraical sum of 11a ...
Page 13
... conveniently effected by the following rule : Rule . Arrange the expressions in lines so that the like terms may be in the same vertical columns : then add each column beginning with that on the left . 3a - 5b + 2c 2a + 3b - 4a + 2b a ...
... conveniently effected by the following rule : Rule . Arrange the expressions in lines so that the like terms may be in the same vertical columns : then add each column beginning with that on the left . 3a - 5b + 2c 2a + 3b - 4a + 2b a ...
Page 14
... convenient to arrange all expressions in descending or ascending powers of that letter . This will be made clear by the following example . Example 1. Add together 4x - 2x2 + 3x2 ; 3x3 - 9x - x2 ; 3x35x2 + 6x + 7 2x2 - 9x - 8 - 2x3 + ...
... convenient to arrange all expressions in descending or ascending powers of that letter . This will be made clear by the following example . Example 1. Add together 4x - 2x2 + 3x2 ; 3x3 - 9x - x2 ; 3x35x2 + 6x + 7 2x2 - 9x - 8 - 2x3 + ...
Page 16
... subtracted is first enclosed in brackets with a minus sign prefixed , then on removal of the brackets the like terms are combined by the rules already exclaimed in Art . 20 . It is , however , more convenient to arrange the SUBTRACTION.
... subtracted is first enclosed in brackets with a minus sign prefixed , then on removal of the brackets the like terms are combined by the rules already exclaimed in Art . 20 . It is , however , more convenient to arrange the SUBTRACTION.
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.