Algebra for Beginners |
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Page 2
... third power of and so on . a , a3 ; The number which expresses the power of any quantity is called its index or exponent . Thus 2 , 5 , 7 are respectively the indices of a2 , a3 , a7 . Note . a2 is usually read " a squared " ; a3 is ...
... third power of and so on . a , a3 ; The number which expresses the power of any quantity is called its index or exponent . Thus 2 , 5 , 7 are respectively the indices of a2 , a3 , a7 . Note . a2 is usually read " a squared " ; a3 is ...
Page 3
... third power of a ; that is , the product of the quantities a , a , a . Thus , if a = = 4 , 3a = 3x a = 3 x 4 = 12 ; a3 = a × a × a = 4 × 4 × 4 = 64 . Example 2. If b = 5 , distinguish between 462 and 264 . Here whereas Example 3 . Here ...
... third power of a ; that is , the product of the quantities a , a , a . Thus , if a = = 4 , 3a = 3x a = 3 x 4 = 12 ; a3 = a × a × a = 4 × 4 × 4 = 64 . Example 2. If b = 5 , distinguish between 462 and 264 . Here whereas Example 3 . Here ...
Page 13
... third and fourth columns are brought down without change . Example 2. Add together - - 2ab + 4ac + 5ad ; bc - 3ub + 4ad . 5ab + 6bc - 7ac Sab - 2ab -- 3ab + bc - 2ab + 7bc + 3ac - 2ad + 4ac + 5ad + 4ad + 7ad 5ab + 6bc - 7ac ; Sab + 3ac ...
... third and fourth columns are brought down without change . Example 2. Add together - - 2ab + 4ac + 5ad ; bc - 3ub + 4ad . 5ab + 6bc - 7ac Sab - 2ab -- 3ab + bc - 2ab + 7bc + 3ac - 2ad + 4ac + 5ad + 4ad + 7ad 5ab + 6bc - 7ac ; Sab + 3ac ...
Page 17
... third columns each sign has to be changed . The re - arrangement of terms in the first line is not necessary , but it is convenient , because it gives the result of subtraction in descend- ing powers of x . Subtract EXAMPLES IV . 1. a + ...
... third columns each sign has to be changed . The re - arrangement of terms in the first line is not necessary , but it is convenient , because it gives the result of subtraction in descend- ing powers of x . Subtract EXAMPLES IV . 1. a + ...
Page 29
... third term is the product of the second terms of the two binomial expressions . 4. The middle term has for its coefficient the sum of the numerical quantities ( taken with their proper signs ) in the second terms of the two binomial ...
... third term is the product of the second terms of the two binomial expressions . 4. The middle term has for its coefficient the sum of the numerical quantities ( taken with their proper signs ) in the second terms of the two binomial ...
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.