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)

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