feat: binomial expansion

.gitignore

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+target/

expansion/Cargo.lock

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+# This file is automatically @generated by Cargo.
+# It is not intended for manual editing.
+version = 4
+
+[[package]]
+name = "expansion"
+version = "0.1.0"

expansion/Cargo.toml

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+[package]
+name = "expansion"
+version = "0.1.0"
+edition = "2024"
+
+[dependencies]

expansion/src/main.rs

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+use std::io;
+
+const EXPONENTS: &str = "⁰¹²³⁴⁵⁶⁷⁸⁹";
+
+fn choose(n: u64, r: u64) -> u64 {
+    if r > n-r {
+        return choose(n, n-r);
+    }
+    let mut result = 1;
+    for i in 0..r {
+        result = result * (n - i) / (i + 1);
+    }
+    result
+}
+
+fn superscript(n: i64) -> String {
+    let n = n.to_string();
+
+    let mut combined = String::new();
+    for c in n.chars() {
+        if c == '-' {
+            combined.push_str("-");
+        } else {
+            let pos = c.to_digit(10).unwrap();
+            combined.push(EXPONENTS.chars().nth(pos as usize).unwrap())
+        }
+    }
+
+    combined
+}
+
+fn main() {
+    println!("Enter a, b, and k, separated by a space:");
+    let mut s = String::new();
+    io::stdin().read_line(&mut s).unwrap();
+
+    let nums: Vec<i64> = s.split_whitespace().map(|d| d.parse::<i64>().unwrap()).collect();
+
+    let a = nums[0];
+    let b = nums[1];
+    let k = nums[2];
+
+    let mut pow_a: u32 = k.try_into().unwrap();
+    let mut pow_b: u32 = 0;
+
+    let mut expansion: Vec<String> = vec![];
+
+    for i in 0..k+1 {
+        let mut end = String::new();
+        if pow_b != k as u32 {
+            end = format!("x{}", superscript(pow_a.into()));
+            pow_a -= 1;
+        }
+
+        expansion.push(format!("{} {}", choose(k as u64, i as u64) * (a.pow(pow_a) * b.pow(pow_b)) as u64, end));
+
+        pow_b += 1;
+    }
+
+    println!("{}", expansion.join(" + "));
+}