3. Also of (2x+y) (2x+3y), when x=2, y=3. 5. 2 x-2y when x=3, y=1. Also of (x+y+ z) (x + y − z) (x+z−y), when x = 1, y=3, z=5. 6. Prove that x {y — (z — u)} = x − y + z−u. 7. If a=1, b=2, c=3, prove that a2+b2+c2+2ab+2ac + 2bc6abc=a+b3 + c3, a* + b2 + c2 = 14 (a + 2c), a+b=11c, a2 - 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+3b) (4c − d), (a+b+c−d) (a− 2c+4d), (2b − 3d) (a+b− 3c + d), a2 − b2 + c2 (a3+b3) (a2b+b3c+c3d), and (a+b+c+ d)3 — a3 − b3 — c3 — d3. 9. Find the value of x3-3x2+3x-1, when x=3. G. P. 1 10. Find the value of -x+ √2x-√1-4x, when x = 12. 11. Simplify 2a − [3b + (2b — c) — 4c + {2a − (3b — c — 26)}]. -- 2a-[c¬{a−b+2c}]–[4b−{3c+a−(4a+c−5b)}]. ADDITION. 1. Add together x2 - ax + a2, 2x2 + 3αx-2α2, and x2 + ax + 3a2. m m-2 2. Add together x+4axm1+a2x2¬2, 3x2 + 2a2xTM¬2 + aTM, m-1 2m-2 3. Add together 2 (a+b) − c + d, a + (b − c) − d, 4. Add together a+2c+d, 2a− (b − c) — d, 5. Add together a3 +a2b−ab2+b3, a3 — (a3b+3ab2) — 2b3, and 2a3-a2b+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 a3 {b — (c–d)}, ab {b+(a−c)}, 8. Add together (3a + 2b + c) x, (2a — 3b — 4c) x, 9. Add together ax-by, x-y, and (a− 1) x + (b + 1) y. 10. Add together 2x2+3 (xy — y3), x2 − y (2x+3y), and x (y― 3x) + y2. 11. Add together (a+26) x − (3a−4b)y, 2a(x+y)+b (x−y), and 4ax +3by. 12. Add together a{b-(c–d)}, a−b-(c-d), a+b-c+d, and a-(b+c-d). 13. Add together 2a3 +3a2b— ac2 + c3, a3 + 2ac2 — b3 +3c3, 3ab4ab2-b'c, and b3-3ab2-5ab4c3. 14. Add together 3a-4a3b+7a2b2+ ab3, 2a*+a3b-bab3+b*, and 3ab - 6a2b2 + 5ab3. 15. Add together ab2c+3abc - ab3, abc + 4a3b* + a*b3, and ab3c+2a2 b-bo. 16. Add together a2 — (ab+b2), 2a2 — (3ab — 4b2), 17. Add together 17a3+25ab71ab2 + 286", 161a3 - 13a2b+14ab2 — 51b3, 19a3 - 146a2b+317ab2 — 80b3, and 6a3-23a2b-200ab2+11263. 18. Add together 121a-31a3b+60a2b2 +28ab3 — 40b*, 30a++ 27a3b — 15a2b2+37ab3 + 12b1, and 6a+a3b — 29a2b2 + 8ab3 — 1661. SUBTRACTION. 1. Subtract a-b+c-d, from 2a+b-c+3d. 2. Subtract 2a-3 (b+c), from a -2b+2c. 3. Subtract a {b - (c–d)}, from 2a+3b (2c-d). 4. Subtract a2 + b2 + c2 - d2, from a2-b2-c2 + d2. 5. Subtract a (x + y − z) + b (x − y + z), from (a+b) x + (2a + 3b) y + (a − b) z. 6. Subtract ax + aby + 2b2z, from 3a (ax+by) — b3z. 7. Subtract 24ax-17ax2 + 5x3, from 3a+25a2x - 3αx2+10x3. 8. Subtract 12 (a+b) x − 13 (a - b) y, from 20a (x+2y) — 15b (2x − y). 9. Subtract a + 2b +2 (a − b) − 3 (a — 2b), from 2a+3 (b-a) — 4 (2b — a). 10. Subtract ax3 + bx3y + cxy2+ dy3, from dx3 + cx2y + bxy2 + ay3. 11. Subtract (a + b −c) x3 + (b + c − d) x2y, 12. Subtract x (x2 − xy + 3y2) + y (2x2 + 3xy − 2y3), from xxy-3xy3 + 2y3. 13. Subtract 2a3 — 3a2b+ab2+b3 from 5a3 + a2b− 6ab2 + b3. 14. Subtract a* — 4a3b+6a2b2 — 7ab3 +b3, 15. Subtract 3a + 5ab — a3b3 — 3ab* + 7b3, from 3a5-5ab+2a2b3 + 965. 16. Subtract 7a* — 3(a3b+ab3) + ba, from 9a* - 3a3b — 7 (ab3 — b1). 17. Subtract 256a3-317ab19ab2 - 3663, from 278a3-311a2b-21ab2 + 14b3. MULTIPLICATION. 1. Multiply together a❜xy', ax'y', and a3x3y. 2. Multiply together a - bx + cx2, and a + bx - cœ3. 3. Multiply together a-b+c, a+b-c, and a+b+c. 4. Multiply together x - x3y+x3y3 — x3y3 + x2y* — xy3 +yo, and x+y. |