Binomial Multiply

A set of binomials are multiplied together and must to be simplified to satisfy the win-conditions.

Challenge

In Binomial Multiply the agent must learn to quickly distribute the binomial multiplications and factor out common terms to leave a simplified representation.

Examples

  • (4 + g^2)(9 + e^3) must be simplified to 36 + (4e^3 + (9g^2 + g^2 * e^3))
  • (a + a) * a must be simplified to 2a^2
  • (c + 5) * c must be simplified to c^2 + 5c
  • (i^3 + 2)(i^3 + 9) must be simplified to i^6 + (11i^3 + 18)
  • (3 + 12o)(10 + 8o) must be simplified to 30 + (144o + 96o^2)

Win Conditions

A problem is considered solved when there are no remaining complex terms in the expression.

No Complex Terms

Terms are considered complex when there's a more concise way they could be expressed.

Examples

  • 2 * 4x is complex because it has multiple coefficients which could be simplified to 8x
  • 4x * y * j^2 is not complex despite being verbose because there is only a single coefficient and no matching variables

Example Episode

A trained agent learns to distribute and simplify binomial and monomial multiplications.

Input

(k^4 + 7)(4 + h^2)

k 4 ^ 7 + 4 h 2 ^ + *

Steps

Step Text
initial (k^4 + 7)(4 + h^2)
distributive multiply (4 + h^2) * k^4 + (4 + h^2) * 7
distributive multiply 4k^4 + k^4 * h^2 + (4 + h^2) * 7
commutative swap 4k^4 + k^4 * h^2 + 7 * (4 + h^2)
distributive multiply 4k^4 + k^4 * h^2 + (7 * 4 + 7h^2)
constant arithmetic 4k^4 + k^4 * h^2 + (28 + 7h^2)
solution 4k^4 + k^4 * h^2 + 28 + 7h^2

Solution

4k^4 + k^4 * h^2 + 28 + 7h^2

4 k 4 ^ * k 4 ^ h 2 ^ * + 28 + 7 h 2 ^ * +