Memoization, pased all test cases.

public static int maxPal(string s,int l,int r,int[][] memo){ if(l==r) return 1; if(l>r) return 0;

        if(memo[l][r]!=-1) return memo[l][r];
        if(s[l]==s[r]) {
                memo[l][r]=2+maxPal(s,l+1,r-1,memo);
                return  memo[l][r];
        }
        int left=maxPal(s,l+1,r,memo);
        int right=maxPal(s,l,r-1,memo);
        memo[l][r]=Math.Max(left,right); 
        return   memo[l][r];
} 

static int playWithWords(string s) {
        /*
         * Write your code here.
         */
        int max=0;
        int[][] memo1=new int[s.Length][];
        int[][] memo2=new int[s.Length][];
         for(int j=0;j<s.Length;j++) {
                 memo2[j]=new int[s.Length];
                 memo1[j]=new int[s.Length];
         }
        for(int i1=0;i1<s.Length;i1++){
                for(int i2=0;i2<s.Length;i2++){
                                memo2[i1][i2]=-1;
                                 memo1[i1][i2]=-1;
                }
        }
        for(int i=1;i<s.Length;i++){

                int left=maxPal(s,0,i-1,memo1);
                int right=maxPal(s,i,s.Length-1,memo2);
                max=Math.Max(max,left*right);
        }
        return max;
}

Does arthrogenix works

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