Reduce using like terms

[n-arms]

Description

Trees can be expanded using the distributive property, but in order to reduce them we need to implement like terms.

Implementation

Let v be a variable, a and b be constants: av^b+a'v^b = (a+a')v^b Therefore we need a way to determine both the power and the constant of a term. This requires some standardization for trees. An arbitrary but somewhat consistent system:

• each expression is separated into terms on the top level: a + b + c + d
• each term is composed of variables raised to exponents multiplied by each other and 1 constant:
  • a(x^2)(y^3)
  • ax^2
  • ax^0 = a
• any combination of numbers that can be reduced to a constant are
• the distributive property is used to expand all terms

Math

• 3x + 4x = 7x
• (1+x)(2+x) = 2 + 1x + 2x + x*x = 2 + 3x + x^2

[n-arms]

• [ ] add standardization to trees #8
• [ ] determine the variables and exponents in a term
• [ ] group like terms
• [ ] commutative property of addition to group even more like terms