বীজগাণিতিক সূত্র | Algebra Formula

বর্গ সূত্র 

(a + b)² = a² + 2ab + b²

(a + b)² = (a - b)² + 4ab

(a - b)² = a² - 2ab + b²

(a - b)² = (a + b)² - 4ab

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

a² + b² = (a - b)² + 2ab

a² + b² = (a + b)² - 2ab

a² - b² = (a + b)(a - b)

a² + b² + c² = (a + b + c)² - 2(ab + bc + ca)

4ab = (a + b)² - (a -b)²

ab= [(a + b)/2]² - [(a - b)/2]²

2(a + b)² = (a + b)² + (a - b)²

(a+b)(b+c)(c+a)= ab(a+b) +bc(b+c) +ac(c+a) +2abc

{(a-b)(b-c)(c-a)} = - {a²(b-c) + b²(c-a) +c²(a-b)

(a+b+c)(ab+bc+ca) = a²(b+c) + b²(c+a) + c²(a+b) + 3abc

x² + x(a+b) + ab = (x+a)(x+b) 

2(ab + bc + ca) = (a + b + c)² - (a² + b² + c²)

ঘন সূত্র

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a + b)³ = a³ + b³ + 3ab(a + b)

(a - b)³ = a³ - 3a²b + 3ab² - b³

(a - b)³ = a³ - b³ - 3ab(a - b)

a³ + b³ = (a + b)(a² - ab + b²)

a³ + b³ = (a + b)³ - 3ab (a + b)

a³ - b³ = (a - b)³ + 3ab (a - b)

a³ - b³ = (a - b)(a² + ab + b²)

(a+b+c)³= a³ + b³ + c³ + 3(a + b) (b + c )(c + a)

a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)

যদি a+b+c=0, তখন a³ + b³ + c³ =3abc হবে

a³ + b³ + c³ - 3abc = 1/2(a+b+c){(a-b)² + (b-c)² + (c-a)²}