Binomial Theorem

A perfect square is a number that can be expressed as the square of an integer.
Distributing is the process of of applying the distributive property to an expression (e.g. $a (b + c) = ab + a c$ ).
Expansion form is sum of products (e.g. $a c + a d + b c + b d$ )
- Expansion is the process of applying the distributive property to an expression for rewriting it in expansion form.
Factored form is product of sums (e.g. $(a + b) (c + d)$ )
- Factoringtodo some types
  - Factoring monomials (e.g. $12 x^{2} = (4 x) (3 x)$ )
  - Factoring the gcf from polynomials (e.g. $2 x^{2} + 4 x = 2 x (x + 2)$ )
  - Factoring out binomial factors (e.g. $x (2 x - 1) - 4 (2 x - 1) = (2 x - 1) (x - 4)$ )
A binomial is an algebraic expression that contains two terms.
- (e.g. $a + b$ , $x - y$ , $2 x + 3 y$ , $x^{2} - 4$ )
A trinomial is an expression of the form $x^{2} + b x + c$
(Binomial theorem or binomial expansion) For any $a, b \in R$ and $n \in N$ , we have $(a + b)^{n} = k = 0 \sum n (k n) a^{n - k} b^{k}$
- (Special case) $(1 + x)^{n} = k = 0 \sum n (k n) x^{k}$
- $k = 0 \sum n (k n) = 2^{n}$
- $k = 0 \sum n (- 1)^{k} (k n) = 0$
(Perfect Square Formulas)
- $(a + b)^{2} = a^{2} + 2 ab + b^{2}$
  - $(A x + B)^{2} = (A x)^{2} + 2 A B x + B^{2}$
- $(a - b)^{2} = a^{2} - 2 ab + b^{2}$

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