Multiplication
Square of a Binomial
A special binomial product is the square of a binomial. Consider the following multiplication.
(x + 4)2 is the same as (x + 4)(x + 4)= x2 + 4x + 4x + 16
= x2 + 8x +16.
Notice that the middle terms are the same. Is this a coincidence? Here is another example.
(a – b)2 = (a – b)(a – b) = a2 – ab – ab + b2
= a2 – 2ab + b2.
It looks like the middle terms are the same again. We notice a pattern when squaring binomials. To square a binomial:
- Square the first term
- Add twice the product of both terms
- Add the square of the second term
Example
(x + 10)2= (x)2 + 2(10)(x) + 102 = x2 + 20x + 100