In algebra we come across certain products very frequently. For e.g., (a + b)2, (a + b)3 (a + b + c)2 etc. These are nothing but products of binomials or trinomials. We derive the formulae for these products and apply them whenever necessary. These expansions help us to avoid elaborate multiplications and make calculations quicker.
Expansions
We shall discuss expansions of binomials, trinomials, Formulae
1. a2 + b2 = (a + b)2 - 2ab
2. a2 + b2 = (a - b)2 + 2ab
3. (a + b)2 = (a - b)2 + 4ab
Summary
(a + b) (a - b) = a2 - b2
(x + a) (x + b) = x2 + (a + b)x + ab.
(a + b)3 = a3 + b3 + 3ab (a + b) = a3 + 3a2b + 3ab2 + b3.
