Algebra

Algebra Product Formulas

Sir Sagar0

Algebra Product Formulas

Real numbers: a , b, c

Whole numbers: n , k

1. (a-b)2 = a2 -2ab +b2

2. (a+b)2 = a2 +2ab +b2

3. (a-b)3 = a3-3a2b +3ab2 –b3

4. (a+b)3 = a3+3a2b +3ab2 +b3

5. (a-b)4 =a4 -4a3b +6a2b2-4ab3 +b4

6.(a+b)4 =a4 +4a3b +6a2b2+4ab3 +b4

7. Binomial Formula

(a +b)^{n} = ^{n}\textrm{c}_{0} a^{n} + ^{n}\textrm{c}_{1} a^{n-1}b + ^{n}\textrm{c}_{2} a^{n-2}b^{2} + ….+ ^{n}\textrm{c}_{n-1} a b^{n-1} + ^{n}\textrm{c}_{n} b^{n}, where ^{n}\textrm{c}_{k} = \frac{n!}{k!(n-k)!}

are the binomial coefficients.

 

8. (a + b +c)2 = a2 +b2 + c2 +2ab +2ac + 2bc

9. (a + b +c + ….+ u + v)2 = a2 + b2 +c2 + ….+ u2 + v2 + 2(ab + ac + ..+ au + av +bc + ….+ bu +bv + …+ uv)

 

 

 

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