Formula list of Mathematic
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Formula
☆ Maruf ☆
1.(a + b)² = a² + 2ab + b² 2.(a - b)² = a² - 2ab + b² 3.(a + b)³ = a³ + b³ + 3ab(a + b) or a³ + b³ + 3a²b + 3ab² 4.(a - b)³ = a³ - b³ - 3ab(a + b) or a³ - b³ - 3a²b - 3ab² 5.a³ + b³ = (a + b)(a² - ab + b²) 6.a³ - b³ = (a - b)(a² + ab + b²) 7.(a + b + c) = a² + b² + c² + 2ab + 2bc + 2ca or a² + b² + c² + 2(ab + bc + ca) 8.(a - b - c) = a² + b² + c² - 2ab + 2bc - 2ca or a² + b² + c² - 2(ab - bc - ca) 9.(x + a)(x + b) = x² + (a + b)x + ab 10.x³ + y³ + z³ - 3xyz = (x + y + z)(x² + y² + z² - xy -yz - zx) 11.New (x + y)(a + b) = x(a + b) + y(a + b) 12.New ab³ = a³+3a²b+3ab²+b³ 13.New ab² = a²+2ab+b² 14.New ab + xy = (a0 + x0) + (b + y) 15.New a * b = {(a-2)*b+(2*b)}
☆ Shortcut method of square ☆
ab² = a²+2ab+b² Example:- 16² a=1 b=6 ab² = a²+2ab+b² 16 = 1²+2×1×6+6² = 1+12+36 = 256 1 6 × 1 6 ---------- 9 6 1 6 × ----------- 2 5 6 -----------
☆ Shortcut method of cube ☆
ab³ = a³+3a²b+3ab²+b³ Example 16³ a = 1 b = 6 ab³ = a³+3a²b+3ab²+b³ 16³ = 1³+3×1²×6+3×1×6²+6³ 16³ = 1+18+3×36+216 16³ = 4096 1 6 × 1 6 ---------- 9 6 1 6 × ----------- 2 5 6 ----------- 2 5 6 × 1 6 ---------- 1 5 3 6 2 5 6 × ----------- 4 0 9 6 -----------
☆ Shortcut method of addition ☆
• ab + xy = (a0 + x0) + (b + y) Example 26 + 47 a=2 b=6 x=4 y=7 ab + xy = (a0 + x0) + (b + y) 26 + 47 = (20 + 40) + (6 + 7) 26 + 47 = (60) + (13) 26 + 47 = 73 2 6 + 4 7 ------- 7 3 -------
☆ Square list 2 to 40 ☆
2² = 4 3² = 9 4² = 16 5² = 25 6² = 36 7² = 49 8² = 64 9² = 81 10² = 100 11² = 121 12² = 144 13² = 169 14² = 196 15² = 225 16² = 256 17² = 289 18² = 324 19² = 361 20² = 400 21² = 441 22² = 484 23² = 529 24² = 576 25² = 625 26² = 676 27² = 729 28² = 784 29² = 841 30² = 900 31² = 961 32² = 1024 33³ = 1089 34² = 1156 35² = 1225 36² = 1296 37² = 1369 38² = 1444 39² = 1521 40² = 1600
☆ cube list 2 to 20 ☆
2³ = 8 3³ = 27 4³ = 64 5³ = 125 6³ = 216 7³ = 343 8³ = 512 9³ = 729 10³ = 1000 11³ = 1331 12³ = 1728 13³ = 2197 14³ = 2744 15³ = 3375 16³ = 4096 17³ = 4913 18³ = 5832 19³ = 6859 20³ = 8000
☆ Example of all formula ☆
1.(a + b)² = a² + 2ab + b²
= (3y + 6z)²
= (3y)² + 2×3y×6z + (6z)²
= 9y² + 36yz + 36z²
2.102²
= (100 + 2)²
= a = 100
= b = 2
(a + b)² = a² + 2ab + b²
= (100 + 2)² = (100)² + 2×100×2 + 2²
= (100 + 2)² = 10000 + 400 + 4
= (100 + 2)² = 10404
3.(3a + 8b)³
= a = 3a
= b = 8b
= (a + b)³ = a³ + b³ +3ab(a + b)
= (3a + 8b)³ = (3a)³ + (8b)³ + 3×3a×8b(3a +8b)
= (3a + 8b)³ = 27a³ + 512b³ + 72ab(3a + 8b)
= (3a + 8b)³ = 27a³ + 512b³ + 216a²b + 576ab²
4.(4a + 6b + 9c)²
(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
a = 4a
b = 6b
c = 9c
= (4a + 6b + 9c)²
= (4a)² + (6b)² + (9c)² + 2×4a×6b + 2×6b×9c + 2×9c×4a
= 16a² + 36b² + 81c² + 48ab + 108bc + 72ac
5.9a³ + 6b³
a³ + b³ = (a + b)(a² - ab + b²)
a = 9a
b = 6a
9a³ + 6b³
= (9a + 6b){(9a)² - 9a×6b + (6b)²}
= (9a + 6b)(91a² - 54ab + 36b²)
6.105 × 115
(100 + 5)(100 + 15)
(x + a)(x + b) = x² + (a + b)x + ab
x = 100
a = 5
b = 15
(100 + 5)(100 + 15)
= (100)² + (5 + 15)100 + 5×15
= 10000 + (20)100 + 75
= 10000 + 2000 + 75
= 12075
7.206 × 307
(200 + 6)(300 + 7)
(x + y)(a + b) = x(a + b) + y(a + b)
x = 200
y = 6
a = 300
b = 7
= 200(300 + 7) + 6(300 + 7)
= 60000 + 1400 + 1800 + 42
= 63242
8. 12 * 13
a = 12
b = 13
a * b = {(a-2)*b+(2*b)}
12 * 13 = {(12-2)*13+(2*13)}
156 = {10*13+(26)}
156 = 130 + 26
156 = 156
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