Elements of Algebra

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Macmillan, 1918 - Algebra - 309 pages
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Page 40 - The square of the difference of two numbers is equal to the square of the first, minus twice the product of the first and the second, plus the square of the second.
Page 40 - The product of the sum and the difference of two numbers is equal to the difference of their squares.
Page 83 - A trinomial belongs to this type, ie it is a perfect square, when two of its terms are perfect squares, and the remaining term is equal to twice the product of the square roots of these terms. The student should note that a term, in order to be a perfect square, must have a positive sign.
Page 122 - If the product of two numbers -is equal to the product of two other numbers, either pair may be made the means, and the other pair the extremes, of a proportion.
Page 122 - In any proportion the product of the means is equal to the product of the extremes.
Page 93 - If the numerator and denominator of each fraction is multiplied (or divided) by the same number, the value of the fraction will not change.
Page 47 - To divide a polynomial by a monomial, divide each term of the dividend by the divisor and add the partial quotients.
Page 54 - The process of solving equations depends upon the following principles, called axioms : 1. If equals be added to equals, the sums are equal. 2. If equals be subtracted from equals, the remainders are equal. 3. If equals be multiplied by equals, the products are equal. 4. If equals be divided by equals, the quotients are equal. 5. Like powers or like roots of equals are equal. NOTE. Axiom 4 is not true if the divisor equals zero.
Page 167 - The number of terms is greater by 1 than the exponent of the binomial. 2. The exponent of a in the first term is the same as the exponent of the binomial, and decreases by 1 in each succeeding term.
Page 122 - The mean proportional between two numbers is equal to the square root of their product.

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