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7 - 30. three) = ninety four. 5(98. 7 - 26. three) (e) (2a)/3 = four 92 necessities OF ALGEBRA [CHAP. five (d) zero. seventy fiveí - zero. forty-one = zero. 25/ + 2. 09 (e) zero. 6r - zero. fifty six + 10(1 - zero. 4r) = zero five. sixty four. five. sixty five. five. sixty six. five. sixty seven. resolve the next equations and payment the suggestions: (a) 32a = 640-20a (c) (b) (d) (e) clear up for the indicated image: (a) 3ax = 12, for x (c) , for E (e) 5R - one hundred twenty five = 18, for S (b) v = v0 + gt, for t (d) PV= \2T, for V clear up the subsequent equations and fee the strategies: (a) (c) (b) (d) (e) alternative the given values for the symbols and ascertain the price of the unknown: (a) V = E-5I;E = 122, / = four (b) P = 2(L + h); P = 15, L = four. five (c) «, = 150,fl 2 = three hundred (d) (e) solutions to Supplementary difficulties five. 36. (a) five (b) W (c) 6 (d) 1 (e) g, i f , five. 37. (a) nine (b) -5 (c) three («05 (e)-16 five. 38. (a) -5 (b) zero (c) 14 five. 39. (a) -4 (b) n (c) five. forty. (a)-180 five. forty-one. (a) -x five. forty two. (a) Xy (è) 4800 (A) zero (b) -6a2b3 (d)-12 (e) 1 (e) -1 (d) -40 (c) (c)4x2-xy (c) -30x4/ (¿0-201,600 (e) 14,400 (d) p3q+p2q2 - 4pq (d) -6a3b2c3 (e) -4x2y¿ - 9xy - 1 (e) O. \2x3y2z CHAP. five] necessities OF ALGEBRA (b) 2ac3 (c) -2p2/q ninety three (e) 2b2c3 five. forty three. (a) -5n/m five. forty four. (a) 4x2 - 4xy + y2 (d) \+2at + a2t2 (g) 4x2 + \2xy + 20x + 9y2 + 30y + 25 (b) 9x2 + \2xz + 4z2 (e) r2 + zero. 2r + zero. 01 (h) x2 - y1 - 2y - 1 (c) 16a2 - \6ab + 462 (/) -\6x2 - 56x - forty nine five. forty five. (d) zero. 8/y (a) 8x3 + \2x2y + oxy2 + y3 (d) l+3bt + 3b2t2 + b3t3 (b) I25p3 - 15p2q + I5pq2 - q3 (e) a3 + zero. 3a2 + zero. 03a + zero. 001 (c) 64x3 + 144*2>> + 108xy2 + 21y3 five. forty six. five. forty seven. (a) 9y - Ix + 6 (c) 110a2 - 240a + four (b) -t2 + 5t-4 (d) 5t3 - It2 + t (e) fa2 + 3xy -9x + 2y (a) -6x3 + 4x2 - 2x + four (d) 6x4 - 10x3 + 6x2 -6x + four (b) -9x4 + 6x3 - 3x2 + 6x (e) I5x4y - \0x3y + 5x2y - lOxy (c) 3x4 - 2x3 + x2 - 2x - 3x3y + 2x2y ~xy + 2y five. forty eight. (a) 3x2 + llxy - IQy2 (c) p3q - 2p2 + pq - 2 (b) ISx2 - 9xy - 2y2 (d) 2t3 + 4t2 - t - 2 five. forty nine. (a) -2c + five five. 50. (a) 5x(x - 2y + 3y2') (c) 2a(\ +2bc-c + a2) (b) 3ac(b -\+2d) (d) r2(2r - 1) five. fifty one. five. fifty two. (d)(3y+l)/2 (c) (2ab - 5c)(2ab + 5c) (b) (3xy - 2z)(3xy + 2z) (d) (c) (ab - \)(ab - 1) (a) (v - s)(v - s) (e) i(ff + ? 2)0, - í2)(í, + Í2) (e) (2a - 3b)(2a - 3b)(2a - 36) (d) r(s + 4)(s + four) (a) 2x(x - y)(x + y) (c) 2(m - 1 )(m + 2) (b) 3a(2X-y)(2x + y) (d) (i - 3)(f + five) (/) (p + 5)(p - 2) (a) (2x - 1)(^ + 2) (d) 2(2a + b)(a - b) (g) (4x - 11)(* + three) (b) (3p - 2q)(p + 3q) (e) (3s - 5t)(2s + t) (h) (4x + 1 )(5x - 1 ) (c) (2m - l)(m + 7) (/) (3x + 2)(lx - 1) (i) (3x - 2)(2 - 5x) five. fifty five. (o)2p+16 five. fifty six. (a) no five. fifty seven. (a) (u + v)/uv (b) (\+bf)/d (6)2« (6) no (c) b(a - b) (c) no (d) no (c) (r2q} + q2r^)/(rlr2) 2 (d) 1ML /12 (e)5-3q + 2/q (e) ^(B + b) (a) (4y - x)(4y + x) (b) (3n + five) five. fifty four. (c) -3/n - 2/m (b) 4a + 2 2 five. fifty three. (e) 8u2 + 8uv - 6v2 (e) (x - 7)(x - 1 ) (d) (3x - y)(x - y) (e) (/> -z)2/(p + z) (e) 3amR/2 94 five. fifty eight. necessities OF ALGEBRA (c) (hl - h2)/h2t (a)(q-p)/pq 2 (b) Q(r2 - r, )/5r, r2 five. fifty nine. five. 60. [CHAP. five (e) 2mdh 2 2 (¿0 4mrx/(r - * ) (e) G£/r3 (a) Is1(2p-q)/5r(2p + q) (c) (A) /( V + E)/( V - s) (d) MR2 ß (a) c/l6d (c) M(R\ + R\)/2 (c) 3r/2g (d) eleven OOÄ/(1100 + R) (b) (rf) M = 2.