3. when x = 2. Also of (2a + y) (2x + 3y), when a = 2, y = 3. Also of (x + y + x) (x + y − ≈) (x + x − y), when 6. Prove that a{y − (≈ − u)} = x − y + z − u. 7. İf α = 1, b = 2, c = 3, prove that a2 + b2 + c2+2ab+2ac+2bc6abc a3 + b3 + c3, aa + ba + c1 = 14(a + 2c), ας + 65 = 11c, a2 - ab+b2 = c, = 8. If a = 2, b = 3, c = 5, and d = 6, find the value of the following expressions: (2a+3b) (4cd), (a+b+c - d) (a 2c+ 4d), (2b - 3d) (a + b − 3c + d), a2 – b2 + c2 — ď2, (a3 + b3) (a3b + b3c + c3d), and (a + b + c + d)3 − a3 − b3 — c3 – ď3. 9. Find the value of x3-3x2+3x-1, when x 3. 10. = when = 12. x 11. Replace the radical signs in the following expressions by fractional indices : √ (x + y)3, √ a3x + √ b3x2 + √ c1æ3‚ √√√a, Va√ √c. ADDITION. 1. Add together x2- ax + a2, 2x2+3ax - 2 a3, 2. Add together xTM+4axTM-1+a2xm-2, 3x+2α2xm−2+am, and am-1+ a2xm-2-6a". 3. 4. 5. Add together 2 (a + b) − c + d, a + (b −c) - d, Add together a + 2c+d, 2a (bc) d, Add together a3 + a2b− ab2 + b3, a3 − (a2b+3ab3) — 2b3, and 2a3a2b+2ab2 + b3. 6. Add together a (b + c − d), b(a + d −c), c(a + d−b), and d (b + c − a). 7. Add together a {b (cd)}, ab{b + (a − c)}, 8. Add together (3a + 2b + c)x, (2a-3b-4c) x, and (a + b −c) x. 9. Add together ax-by, x-y, and (a− 1) x + (b + 1)y. 10. — 11. 12. Add together 2x2 + 3 (xy − y3), xo − y (2x + 3y), and x(y − 3x) + y2. Add together (a+2b)x−(3a-4b)y, 2a(x+y)+b(x−y) and 4ax + 3by. Add together a {b−(c–d)},a-b-(c–d), a+b−c+d, 13. Add together 2 a3+3a2b- ac2 + c3, a3 +2 ac2 — b3 + 3 c3, 3a2b+4ab2 - b3c, and b3 – зab2 - 5a2b - 4c3. 14. 15. Add together sa1—4a3b+ab3+7a2b3,2a1+a3b-6ab3+ba, and 3ab5ab3 - 6a2b2. Add together a2b3c2 — a1b2 + 3 ab3c3, abc1 + 4a2b1 + a1b3, and ab3c+2a2b1 — bo. 16. Add together a2 − (ab + b2), 2a3 — (3ab−4b2), and 4ab3bo. 17. Add together 17a3+25ab71ab2 + 28b3, 161 a3-13a2b+14ab25163, 19a3 - 146ab + 317 ab2 - 80b3, and 6a3-23 a2b - 200 ab2 + 112b3. 18. a1 Add together 121 a 31 ab + 60 a2b2 + 28 a b3 - 40 b1, Subtract ab+ cd, from 2a+b-c+ 3d. 1. 2. Subtract 2a 3 (b + c), from a − 2b + 2c. 3. Subtract a (x + y − x) + b (x − y + x), from (a + b) x + (2a + 3b) y + (a − b)x. 4. Subtract ax+aby+2bx, from 3a (ax+by) - b'x. 5. Subtract 24a x 17a x2+5x3, 6. from 3a+25a2x-3a x2+10x3. − Subtract 12 (a + b) x 13 (a - b) y, + 2 y) − 15b (2x − y). 7. Subtract 3ab + 4a3 – 5b3, from 3a +9aba. 8. Subtract a + 2 b + 2 (a - b) — 3 (a - 2b), from 2a + 3 (b− a) — 4 (2b − a). 9. Subtract ax3 + bx2y + cxy2 + dy3, 10. 11. 12. from da3 + ca2y + bx y2 + ay3. Subtract (a + b − c) x3 + (b + c − d) x2y, Subtract x (x2- xy + 3y3) + y (2x2 + 3xÿ − 2y3), Subtract a - {b 13. Subtract 2a3-3a2b+ab+b3, from 5a3 + a3b − 6ab2+b3. Subtract a2+b2 + c2 - d, from a b2 - c2 + d2. 18. Subtract 256 a3-317a2b+19ab2 - 36b3, from 278a3311ab21 ab2 + 14b3. MULTIPLICATION. 1. Multiply together a2xy3, ax2y3, and a3x3y. 2. Multiply together ala, ax, and axl. 3. Multiply together a bx + ca2, and a + bx − cx2. 4. Multiply together a − b + c, a + c − b, and a + b + c. · 4 5. Multiply together x − xy + x1y2 — x3y3 + x2y1 — xy3+yo, and x + y. 6. Multiply together 2a3b+3a2b2 — ab3 + 4b1, and a 4a3b+ a2b2 - 3ab3. 7. Multiply together x1- 2x3y + 4x2 y2 − 8xy3 + 16y1, and x2-2y3. 8. Multiply together x2 - 2x + 3, and ∞2 − ∞ + 1. 9. Multiply together aa +2, and x + 3æ3 − 1. 10. Multiply together am+- xm+n ym+n + ym+n, 11. Multiply together a2+b2+c2-ab-ac-bc, and a+b+c. 12. Multiply together a1 (b − c) + a3 (ab − bc), and a (ab+bc). 13. Multiply together x 1, x2, and ≈ – 3. 14. Multiply together a2 - 2x + 1, x2 + 2x + 1, 15. Multiply together xa, ab, and x – c. 16. Multiply together a + b, a − b, a2 - ab + b2, and a2 + ab + b2. |