Expansion of binomial products
The distributive law says that for any numbers A,B, and C, A\left(B+C\right)=AB+AC. However A can also be an expression in brackets, and the distributive law still holds.
Consider the expression \left(A+B\right)\left(C+D\right). If we want to expand this using the distributive law we get A\left(C+D\right)+B\left(C+D\right). If we then expand the brackets in both terms we get AC+AD+BC+BD. That is, \left(A+B\right)\left(C+D\right)=AC+AD+BC+BD.
Examples
Example 1
Expand \left(x+10\right)\left(x+5\right)
Example 2
Expand the following perfect square: \left(x+2\right)^2
Example 3
Expand the following:
\left(m+3\right)\left(m-3\right)
We can expand the product of two binomial expressions using the rule
\left(A+B\right)\left(C+D\right)=AC+AD+BC+BD.
There are two special cases of expanding binomials:
\left(A+B\right)^2=A^2+2AB+B^2(called a perfect square)
\left(A+B\right)\left(A-B\right)=A^2-B^2(called a difference of two squares)