First Lessons in Algebra; Embracing the Elements of the Science
This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1839 edition. Excerpt: ...how are the signs of the terms 1 Of the Exponents. 88. The letter which occupies the first place in a binomial, is called the leading letter. Thus, a is the leading letter in the binomials a--b. 1st. It is evident that the exponent of the leading letter in the first term will be the same as the exponent of the power; and that this exponent will diminish by unity in each term to the right, until we reach the last term, which does not contain the leading letter. 2nd. The exponent of the second letter is 1 in the second term, and increases by unity in each term to the right, until we reach the last term, in which the exponent is the same as that of the given power. 3rd. The sum of the exponents of the two letters, in any term, is equal to the exponent of the given power. This last remark will enable us to verify any result obtained by the binomial theorem. Let us now apply these principles in the two following examples, in which the coefficients are omitted: --(a+b)s... aS + aSb+cttf+aW+aW+abs+b6, (a--b)e... a--a5b+abi--aib3+a%l--ab!'+bi. As the pupil should be practised in writing the terms without the coefficients and signs, before finding the coefficients, we will add a few more examples. Quest.--88. Which is the leading letter of the binomial 1 What is the exponent of this letter in the first term 1 How does it change in the terms towards the right1 What is the exponent of the second letter in the second term 1 How does it change in the terms towards the right1 What is it in the last term 1 What is the sum of the exponents in any term equal to 1 1. (a+b)3.. a3 + a2b + ab2 + b3. 2. (a--by.. tf--rfb+aW-aP+b. 3. (a+bf.. a6+a6+a362+a263+a64+68. 4. (a-Z)7.. a?-aSb+aW-atP + aW-aW Of the Coefficients. 89. The coefficient of the first term is...
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- 13 Sep 2013
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