Addition of Algebraical Ties

ADDITION OF ALGEBRAICAL TIES.

The addition of altrebraical quantities. is 5erformed by connecting those that are un ike with their proper sigma, and collecting 'hose that are similar into one sum. , Add together the following unlike pantities : Ex. 1 a x +3.: --2 y Ans. ax—btt+ y Ex. :2 — a-Fb z—zr —4y+.3 c Ans. —a+ b+3 c—x-4 It is immaterial in what order the quan tities are set clown, if WC take care to prefix to each its proper sign.

When any terms are similar, they may be incorporated, and the general expres sion for the sum shortened.

1. When similar quantities have the same sign, their sum is found by taking the SUM of the co-efficients with that sign, and annexing the common letters.

Ex. 3. 4 a-5 b2 a — 6 b 9 a —3 b Ans. 15 a-14 b Ex. 4. eta' c —10 bde 6a'c— 9bde lla'r— fib de Ans. 21a=c - 22bde The reason is evident ; 4 a to be add ed, together with 2 a and 9 a to be add ed, makes 15 a to be added ; and 5 b to be subtracted, together with 6 b and 3 a to be suptracted, is 14. b to be subtract ed.

2. If similar quantities have different sig-ns, their sum- is found by taking the lifference of the co-efficients with the 5ign of the greater, and annexing the :ommon letters as before.

Ex. 5. 7 a +3 h — 5 a-9 b Ans. 2 a-6 b Ex. 6. 6 a+46-3- 9 c — 9 aχ3 b+16 c +12 a-76--20 c Ans. 9a • + 5 c

— In the first part of' the operation we have 7 times a to add, and 5 times a to ,ake away; therefore, upon the whole, we have 2 a to add. In the latter part, we have 3 times b to add, and 9 times b :o take away; e. we have, upon the whole, 6 times b to take away: and thus le sum of all the quantities is 20 —6b. If several similar quantities are to bc tdded together, some with positi. e and Rune with negative signs, take the differ ence between the sum of the positive and the sum of the negative co-efficients, prefix the sign of the greater sum, and annex the common letters.

Ex. 7. 3 + 4 b — -I- 10 x — 23 —5 a' — 15x+ 44 — 4 a' — 9 c —10e' +21 x — 9(1 Ans. — 6 + b c — 9 e' + 16 x —71 Ex. 8. -4 ac —15bd+ex —ax 11 ac+ 76' —19ex-1-4a .r -- 41 a' + 6 bd— 7 tle-2a A.15ac —41a'-9'd+75'-18ex-7tle—ax Ex. 9. p xs — q — ). a — Ans. p-I-a ..r3— 9+8 — r+ 1..r In this example, the co-efficients of x and its powers are united ; p+a . X3=p +a s' ; also — q+b s'=-. — 9 x'— b u-', because the negative sign affects the whole quantity under the vinculum ; and — r —1 . x= — r x—x