Algebra for Beginners: With Numerous Examples

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Macmillan and Company, 1872 - 328 σελίδες

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Σελίδα 27 - expressions ; multiply each term of the multiplicand by each term of the multiplier; if the terms have the same sign prefix the sign + to the product, if they have different signs prefix the sign —; then collect these results to form the complete product.
Σελίδα 126 - A cask, A, contains 12 gallons of wine and 18 gallons of water ; and another cask, В, contains 9 gallons of wine and 3 gallons of water: how many gallons must be drawn from each cask so as to produce by their mixture 7 gallons of wine and 7 gallons of water? Let
Σελίδα 36 - descending powers of some common letter. Divide the first term of the dividend by the first term of the divisor, and put the result
Σελίδα 211 - 3 , which is three times the square of the part of the root already found. Now divide the remainder in the third column by the expression just obtained, and we arrive at
Σελίδα 129 - Divide the number 90 into four parts such that the first increased by 2, the second diminished by 2, the third multiplied by 2, and the fourth divided by 2 may all be equal
Σελίδα 129 - Suppose the distance between London and Edinburgh is 360 miles, and that one traveller starts from Edinburgh and travels at the rate of 10 miles an hour, while another starts at the same time from London and travels at the rate of 8 miles an hour : it is required to know where they will meet.
Σελίδα 260 - binomial factors which are multiplied together. II. The exponent of x in the first term is the same as the number of binomial factors, and in the other terms each exponent is less than that of the preceding term by unity. III. The coefficient of the first term is unity;
Σελίδα 167 - is unity, the sum of the roots is equal to the coefficient of the second term with its sign changed, and the product of the roots is equal to the last term. For
Σελίδα 258 - To find the number of permutations of n things taken all together which are not all different. Let there be n letters ; and suppose p of them to be a, q of them to be b, r of them to be c, and the rest
Σελίδα 94 - A letter to which a particular value or values must be given in order that the statement contained in an equation may be true, is called an unknown quantity. Such particular value of the unknown quantity is said to satisfy the equation, and is called a root of the equation. To solve an equation is to find the root or roots.

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