(i) 3x² × 11xy × (2/3)y²:
= [3 × 11 × (2/3)] × (x² × x) × (y × y²)
= 22x³y³

(ii) (-5x) × 3a² × (-3ax):
= [(-5) × 3 × (-3)] × (a² × a) × (x × x)
= 45a³x²

(iii) (-3pq) × (-15p³q³) × q²:
= [(-3) × (-15)] × (p × p³) × (q × q³ × q²)
= 45p⁴q⁶

(iv) 3x(5x² + 8):
= (3x × 5x²) + (3x × 8)
= 15x³ + 24x

(v) (2/3)y(18y² - y):
= [(2/3)y × 18y²] - [(2/3)y × y]
= 12y³ - (2/3)y²

(vi) (-8a³)(a + 3b + 2c):
= (-8a³ × a) + (-8a³ × 3b) + (-8a³ × 2c)
= -8a⁴ - 24a³b - 16a³c

(vii) (3mn - 2n)(-2m²n):
= [3mn × (-2m²n)] - [2n × (-2m²n)]
= -6m³n² + 4m²n²

(viii) (9x² + 4x + 3) × 11x:
= (9x² × 11x) + (4x × 11x) + (3 × 11x)
= 99x³ + 44x² + 33x

(ix) (20a² - 3b² + ab) × (-7b²):
= -140a²b² + 21b⁴ - 7ab³

(x) 3x³y²(xy + xy³ - 2):
= 3x⁴y³ + 3x⁴y⁵ - 6x³y²

(i) (x² + y)(3x²y - y²):
= x²(3x²y - y²) + y(3x²y - y²)
= 3x⁴y - x²y² + 3x²y² - y³ = 3x⁴y + 2x²y² - y³

(ii) (7x - 2y)(2x + 7y):
= 7x(2x + 7y) - 2y(2x + 7y)
= 14x² + 49xy - 4xy - 14y² = 14x² + 45xy - 14y²

(iii) (¼a² + 3b)(a³ + ⅔b²):
= ¼a²(a³ + ⅔b²) + 3b(a³ + ⅔b²)
= ¼a⁵ + (1/6)a²b² + 3a³b + 2b³

(iv) (1.5x - 2.5y)(2.5x - 1.5y):
= 1.5x(2.5x - 1.5y) - 2.5y(2.5x - 1.5y)
= 3.75x² - 2.25xy - 6.25xy + 3.75y² = 3.75x² - 8.5xy + 3.75y²

(v) (3x + 4y)(2x² + 3y + xy):
= 3x(2x² + 3y + xy) + 4y(2x² + 3y + xy)
= 6x³ + 11x²y + 4xy² + 9xy + 12y²

(vi) (2xy + 5x²)(x⁵y⁴ - x³y² + xy):
= 5x⁷y⁴ + 2x⁶y⁵ - 5x⁵y² - 2x⁴y³ + 5x³y + 2x²y²

(vii) (3a²b² - 4c)(a³b³ + 2a⁴b³c³ - 6abc):
= 6a⁶b⁵c³ + 3a⁵b⁵ - 8a⁴b³c⁴ - 22a³b³c + 24abc²

(viii) (4x²y - 5xy² + 3xy)(3x³y - 2):
= 12x⁵y² - 15x⁴y³ + 9x⁴y² - 8x²y + 10xy² - 6xy

(ix) (2x + 3y + z)(5x + 2y + 1):
= 10x² + 19xy + 5xz + 2x + 6y² + 2yz + 3y + z

(x) (3x³ - 2y² + z)(3x³ + 2y² - z):
= [3x³ - (2y² - z)][3x³ + (2y² - z)]
= (3x³)² - (2y² - z)² = 9x⁶ - 4y⁴ + 4y²z - z²

(i) 3x(5x + 8) - 10x:
= 15x² + 24x - 10x
= 15x² + 14x

(ii) (2m + 3m²)(-2mn):
= [2m × (-2mn)] + [3m² × (-2mn)]
= -4m²n - 6m³n

(iii) 8(3a + 4b) + 5:
= (8 × 3a) + (8 × 4b) + 5
= 24a + 32b + 5

(iv) 2x²(4x - 1) + 3x(x - 3):
= 8x³ - 2x² + 3x² - 9x
= 8x³ + x² - 9x

(i) (p + q²)(q² - p) + 15:
= (q² + p)(q² - p) + 15 = (q²)² - p² + 15
= q⁴ - p² + 15

(ii) (a - b)(a² + ab + b²) + 3b³:
= (a³ - b³) + 3b³
= a³ + 2b³

(iii) y²(y³ + 3x) + y(2xy + y²):
= y⁵ + 3xy² + 2xy² + y³
= y⁵ + y³ + 5xy²

(iv) [(2/3)x⁴y³ + (4/9)xy³] × ¼ - (1/6)x⁴y³:
= (1/6)x⁴y³ + (1/9)xy³ - (1/6)x⁴y³
= (1/9)xy³

(v) y³(4y + 5) - (2y + 1)(y³ + 2y² + 1):
= (4y⁴ + 5y³) - (2y⁴ + 4y³ + 2y + y³ + 2y² + 1)
= 4y⁴ + 5y³ - 2y⁴ - 5y³ - 2y² - 2y - 1
= 2y⁴ - 2y² - 2y - 1

(vi) (1.2l - 2.5m)(2.5l + 0.2m + 1.2) + 0.06l + 7m:
= 3l² + 0.24lm + 1.44l - 6.25lm - 0.5m² - 3m + 0.06l + 7m
= 3l² - 6.01lm + 1.5l - 0.5m² + 4m

(i) (x + 7)(x + 5):
= x² + (7 + 5)x + (7 × 5)
= x² + 12x + 35

(ii) (7x + 2y)(7x + 6y):
= (7x)² + (2y + 6y)(7x) + (2y × 6y)
= 49x² + 8y(7x) + 12y² = 49x² + 56xy + 12y²

(iii) (4x³ + 8)(4x³ + 10):
= (4x³)² + (8 + 10)(4x³) + (8 × 10)
= 16x⁶ + 72x³ + 80

(iv) (4k² - 3k)(4k² - 7k):
= (4k²)² + [(-3k) + (-7k)](4k²) + [(-3k) × (-7k)]
= 16k⁴ - 40k³ + 21k²

(v) (a/2 + ½)(a/2 - ¼):
= (a/2)² + (½ - ¼)(a/2) + [½ × (-¼)]
= a²/4 + a/8 - 1/8

(vi) (n²/5 - 0.6)(n²/5 + 1.6):
= (n²/5)² + (-0.6 + 1.6)(n²/5) + [(-0.6) × 1.6]
= n⁴/25 + 0.2n² - 0.96

(vii) 98 × 97:
= (100 - 2)(100 - 3)
= 100² + [(-2) + (-3)](100) + [(-2) × (-3)]
= 10000 - 500 + 6 = 9506

(viii) 501 × 503:
= (500 + 1)(500 + 3)
= 500² + (1 + 3)(500) + (1 × 3)
= 250000 + 2000 + 3 = 252003

(i) (x + 5)²:
= x² + 2(x)(5) + 5² = x² + 10x + 25

(ii) (5x + 4y)²:
= (5x)² + 2(5x)(4y) + (4y)² = 25x² + 40xy + 16y²

(iii) (3a³ + 4a²)²:
= (3a³)² + 2(3a³)(4a²) + (4a²)² = 9a⁶ + 24a⁵ + 16a⁴

(iv) (3x + 1/3x)²:
= (3x)² + 2(3x)(1/3x) + (1/3x)² = 9x² + 2 + 1/9x²

(v) (p/q + q/p)²:
= (p/q)² + 2(p/q)(q/p) + (q/p)² = p²/q² + 2 + q²/p²

(vi) 502²:
= (500 + 2)² = 500² + 2(500)(2) + 2²
= 250000 + 2000 + 4 = 252004

(vii) (9.5)²:
= (9 + 0.5)² = 9² + 2(9)(0.5) + (0.5)²
= 81 + 9 + 0.25 = 90.25

(viii) (4⅛)²:
= (4 + 1/8)² = 4² + 2(4)(1/8) + (1/8)²
= 16 + 1 + 1/64 = 17 1/64

(i) (x - 7)²:
= x² - 2(x)(7) + 7² = x² - 14x + 49

(ii) (6x - 5)²:
= (6x)² - 2(6x)(5) + 5² = 36x² - 60x + 25

(iii) (10x² - 3y)²:
= (10x²)² - 2(10x²)(3y) + (3y)² = 100x⁴ - 60x²y + 9y²

(iv) (p² - q²)²:
= (p²)² - 2(p²)(q²) + (q²)² = p⁴ - 2p²q² + q⁴

(v) (a²x - ax²)²:
= (a²x)² - 2(a²x)(ax²) + (ax²)² = a⁴x² - 2a³x³ + a²x⁴

(vi) (x² - 1/x²)²:
= (x²)² - 2(x²)(1/x²) + (1/x²)² = x⁴ - 2 + 1/x⁴

(vii) 296²:
= (300 - 4)² = 300² - 2(300)(4) + 4²
= 90000 - 2400 + 16 = 87616

(viii) 1999²:
= (2000 - 1)² = 2000² - 2(2000)(1) + 1²
= 4000000 - 4000 + 1 = 3996001

(i) (y + 11)(y - 11):
= y² - 11² = y² - 121

(ii) (2x + 3)(2x - 3):
= (2x)² - 3² = 4x² - 9

(iii) (6 + m²)(m² - 6):
= (m² + 6)(m² - 6) = (m²)² - 6² = m⁴ - 36

(iv) (ax² - by)(ax² + by):
= (ax²)² - (by)² = a²x⁴ - b²y²

(v) (1 - xᵐ)(1 + xᵐ):
= 1² - (xᵐ)² = 1 - x²ᵐ

(vi) 61 × 59:
= (60 + 1)(60 - 1) = 60² - 1² = 3600 - 1 = 3599

(vii) 106 × 94:
= (100 + 6)(100 - 6) = 100² - 6² = 10000 - 36 = 9964

(viii) 9.5 × 8.5:
= (9 + 0.5)(9 - 0.5) = 9² - (0.5)² = 81 - 0.25 = 80.75

(i) (3x - 5m)(3x - 5m) = (3x - 5m)²:
= (3x)² - 2(3x)(5m) + (5m)² = 9x² - 30mx + 25m²

(ii) (4m + 3)(4m + 2):
= (4m)² + (3 + 2)(4m) + (3 × 2) = 16m² + 20m + 6

(iii) (9 + 4n)²:
= 9² + 2(9)(4n) + (4n)² = 81 + 72n + 16n²

(iv) (6x + ⅓)(6x + 3):
= (6x)² + (⅓ + 3)(6x) + (⅓ × 3)
= 36x² + (10/3)(6x) + 1 = 36x² + 20x + 1

(v) (x - x/2)² = (x/2)²:
= x²/4

(vi) (4ab - c)(4ab + c):
= (4ab)² - c² = 16a²b² - c²

(vii) (a²/2 + b²/4)²:
= (a²/2)² + 2(a²/2)(b²/4) + (b²/4)²
= a⁴/4 + a²b²/4 + b⁴/16

(viii) (0.5x² - 0.2y²)²:
= (0.5x²)² - 2(0.5x²)(0.2y²) + (0.2y²)²
= 0.25x⁴ - 0.2x²y² + 0.04y⁴

(ix) (y³ - 9x²)(y³ + 9x²):
= (y³)² - (9x²)² = y⁶ - 81x⁴

(x) (y²/2 - 4)(y²/2 + 6):
= (y²/2)² + (-4 + 6)(y²/2) + (-4 × 6)
= y⁴/4 + y² - 24

(xi) (7x² + ⅓)²:
= (7x²)² + 2(7x²)(⅓) + (⅓)² = 49x⁴ + (14/3)x² + 1/9

(xii) [(x + y) + z][(x + y) - z]:
= (x + y)² - z² = x² + 2xy + y² - z²

(xiii) 1002 × 999:
= (1000 + 2)(1000 - 1) = 1000² + (2 - 1)(1000) + [2 × (-1)]
= 1000000 + 1000 - 2 = 1000998

(xiv) (10.2)²:
= (10 + 0.2)² = 10² + 2(10)(0.2) + 0.2²
= 100 + 4 + 0.04 = 104.04

(xv) 79²:
= (80 - 1)² = 80² - 2(80)(1) + 1²
= 6400 - 160 + 1 = 6241

(xvi) 6.2 × 5.8:
= (6 + 0.2)(6 - 0.2) = 6² - (0.2)²
= 36 - 0.04 = 35.96

(i) (x + 1/x)(2x + 1/x):
= 2x² + 1 + 2 + 1/x² = 2x² + 3 + 1/x²

(ii) (2l + m)² - (2l - m)²:
= 4 × (2l) × m = 8lm

(iii) (a²b + ab²)² - 6a³b³:
= a⁴b² + 2a³b³ + a²b⁴ - 6a³b³
= a⁴b² - 4a³b³ + a²b⁴

(iv) (x² - y²) + (y² - z²) + (z² - x²):
= 0

(v) (5a - 6b)² + 20ab - (6b + 5a)²:
= (5a - 6b)² - (5a + 6b)² + 20ab
= -4(5a)(6b) + 20ab = -120ab + 20ab = -100ab

(vi) (16p⁴ - 25q⁴) + (4p⁴ - 20p²q² + 25q⁴):
= 20p⁴ - 20p²q²

(vii) (2x - 5)(2x + 3) - (x - 2)² + 29:
= (4x² - 4x - 15) - (x² - 4x + 4) + 29
= 4x² - 4x - 15 - x² + 4x - 4 + 29 = 3x² + 10

(viii) (x²/9 - 9y²/16) + (9y²/16 + 3xy + 9x²y/4?):
= (x²/9 - 9y²/16) + (9y²/16 + 3xy + 3x²)
= x²/9 + 3x² + 3xy = (28/9)x² + 3xy

(ix) [ (x+y)/5 + (x-y)/5 ]²:
= (2x / 5)² = 4x²/25

(x) 2.89² + 2(2.89)(0.11) + 0.11²:
= (2.89 + 0.11)² = 3² = 9

(xi) (0.5² - 2×0.5×3.5 + 3.5²) / 3:
= (0.5 - 3.5)² / 3 = (-3)² / 3 = 9 / 3 = 3

(xii) (4.68² - 3.32²) / 1.36:
= (4.68 - 3.32)(4.68 + 3.32) / 1.36
= (1.36 × 8.0) / 1.36 = 8