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ALGEBRA.

USE OF SYMBOLS.

ERRATA.

Page 12, Ex. IT, in the answer, for – 33+4, read + 32 – 4.

68, Ex. 35, for or, read so.
72, Ex. 24, for T, V, read V.
96, Ex. 4, omit there are three directions, in any one of which ; and,

after the word struck, read in any direction, so that it strike

the sides successively. 102, Ex. 9, for the length of the diameter : the length of the semicircle,

read 2 : 1 - 2.

Ex. 12, for at A, read at P.
103, Ex. 24, for distance, read distances.
106, Ex. 15, for is proportional, read is inversely proportional.

a' - ab + b = c,

(a + b)(a + c) (6 + c) = 10abc. 8. If a=2, b = 3, c= 5, and d=6, find the value of the following expressions : (2a +36) (4c – d), (a +b+c-d) (a– 2c +4d), (26 3d) (a + b 3c+d), a* - 72 + c - ď", (ap + 38) (ab + 6*c+c®d), and (a + b +c+d) - a— 73 — * -d8.

9. Find the value of 203 - 3x + 30 – 1, when = 3.
G. P.

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3. Also of (2x+y) (2x + 3y), when x = 2, y = 3.
4. Also of
2002 + y2 23c 42

when =3, y=1. 3+ 2y 2y 5. Also of (c + y +z) (x+yz) (x +%-y), when x = 1, y= 3,2=5.

6. Prove that a – {y-(2 – u)} = x y +% — U.
7. If a=1, b=2, c=3, prove that

a + b +0+ 2ab + 2ac + 2bc = 6abc = a +58 +0,
a* + 74 + 4 = 14 (a +2c),
+ 38 = 11c,
a' - ab + b2 = c,

(a + b) (a + c)(b + c) = 10abc. 8. If a=2, b=3, c=5, and d=6, find the value of the following expressions: (2a +36) (4c d), (a +b+c-d) (a– 2c +4d), (26 — 3d) (a + b – 3c+d), a? — 3* + c* — d, (as +39) (a+b+ b*c +ced), and (a + b +c+d)! – Q3 – 68 – 08 – do. 9. Find the value of x - 300 + 3x – 1, when x= 3.

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G. P.

10. Find the value of Ji - x + 2x – J1 - 4x, when = 1. 11. Simplify 2a - [36+ (21 – c) – 4c+ {2a – (36-C – 26)}]. 12.

2a-[c-za-b+2c}]–[46–{3c+a-(4a+c-56)}].

ADDITION.

1. Add together xc - ax + a', 2x + 3ax - 2a”,

and 2 + ax + 3a".

2. Add together 2c" + 4ax"-1 + a a"-9, 33" + 2a oc"+ a",

and accm-1 + a 2-2 - 6a".

3. Add together 2 (a+b) – c+d, a + (6 —c) – d,

and a +b-c-d). 4. Add together a + 2c+d, 2a (6-0) d,

and 3a + b - (3c+d).

5. Add together ai +aob - ab? + 6%, ai – (a%b + 3ab?) 25,

and 2a: - ab + 2ab + 73.

6. Add together a (b +c-d), b(a + d-c), c(a + d-6),

and d (6+c-a). 7. Add together a' {6 - (c-d)}, ab {b + (a - c)},

and b (c+d - a). 8. Add together (3a + 2b+c) 2, (20 – 36 – 40) x,

and (a + b -c) .. 9. Add together ax by, y, and (a – 1) x + (6+1) y. 10. Add together 2x + 3 (wy - y2), x y (2x + 3y),

and » (y - 3x) + y. 11. Add together (a +26) x — (3a-46)y, 2a(x+y)+(xy),

and 4ax + 3by.

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