Basic Maths Formulas – Algebra
Common Formula’s in Maths
Square Formula’s
1. (a + b) 2 = (a) 2 + (b) 2 + 2ab
2. (a – b) 2 = (a) 2 + (b) 2 – 2ab
3. (a) 2 – (b) 2 = (a + b)(a – b)
4. (x + a) (x + b) = x2 + (a + b)x + ab
5. (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
6. (a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
7. (a + (-b) + (-c))2 = a2 + (-b)2 + (-c)2 + 2a(-b) + 2(-b)(-c) + 2a(-c)
8. (x + y) 2 = (x) 2 + (y) 2 + 2xy
9. (x – y) 2 = (x) 2 + (y) 2 – 2xy
10. (x) 2 – (y) 2 = (x + y)(x – y)
11. (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2xz
12. (x – y – z)2 = x2 + y2 + z2 – 2xy + 2yz – 2zx
13. (x + (-y) + (-z))2 = x2 + (-y)2 + (-z)2 + 2x(-y) + 2(-y)(-z) + 2x(-z)
Cube Formula’s
1. (a + b) 3 = a3 + b3 + 3ab(a + b)
2. (a + b) 3 = a3 + b3 + 3a2b + 3ab2
3. (a – b) 3 = a3 – b3 – 3ab(a – b)
4. (a – b) 3 = a3 – b3 – 3a2b + 3ab2
5. (a + b +c) 3 = a3 + b3 + c3 +3ab(a + b)(b + c)(c + a)
6. a3 + b3+ c3 -3abc = (a + b + c)(a 2 + b 2 + c 2
-ab – bc – ca)
7. (x + y) 3 = x3 + y3 + 3xy(x + y)
8. (x – y) 3 = x3 – y3 – 3xy(x – y)
9. (x + y +z) 3 = x3 + y3 + z3 +3xy(x + y)(y + z)(z + x)
10. x3 + y3+ z3 -3xyz = (x + y + z)(x 2 + y 2 + z 2
-xy – yz – zx)
11. a3 – b3 = (a – b)(a 2 + ab + b2)
12. a3 + b3 = (a + b)(a 2 – ab + b2)
Fourth and Fifth Power Formula’s
13. (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4
14. (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4
15. a4 – b4 = (a – b)(a + b)(a 2 + b2)
16. a5 – b5 = (a – b)(a 4 + a3b + a2b2 + ab3+ b4)