Algebraic Expressions

Factoring and expanding algebraic expressions, rules for transforming algebraic expressions
Using a variety of methods including combinations of the above to factorize algebraic expressions
Factoring and expanding algebraic expressions, rules for transforming algebraic expressions
Expanding algebraic expressions
The square of a binomial, a perfect square trinomial
 (a + b)2 = a2 + 2ab + b2 (a - b)2 =  a2 - 2ab + b2
The square of a trinomial
 (a - b + c)2 = a2 + b2 + c2 - 2ab + 2ac - 2bc
The cube of a binomial
 (a + b)3 = a3 + 3a2b + 3ab2 + b3 (a - b)3 = a3 - 3a2b + 3ab2 - b3
The binomial expansion algorithm - the binomial theorem
Factoring algebraic expressions
Difference of two squares
 x2 - y2 = (x - y) · (x + y)
Sum and difference of cubes
 x3 - y3 = (x - y) · (x2 + xy + y2) x3 + y3 = (x + y) · (x2 - xy + y2)
The sum and/or difference of any two numbers raised to the same (positive integer) power
 x4 - y4 = (x - y) · (x3 + x2y + xy2 + y3) = (x2 - y2) · (x2 + y2)
 x2n - y2n = (x - y) · (x2n-1 + x2n-2y + ¼  + xy2n-2 + y2n-1) = (xn - yn) · (xn + yn)