By the Binomial Theorem: <span>(a + b)^n = sum(k=0 to n) [C(n, k) * a^(n - k) * b^k]. </span> By letting a = 2x, b = 3, and n = 9 <span>(2x + 3)^9 = sum(k=0 to 9) [C(9, k) * (2x)^(9 - k) * 3^k]. </span>As you can see, the power of x is 9 - k. Since we want the x^6 term: <span>9 - k = 6 ==> k = 3 </span>Thus, letting k = 3 yields the term containing x^6 to be: <span>C(9, 6) * (2x)^(9 - 3) * 3^4 = 435456x^6. </span> <span>. </span>