Question

use pascals triangle to complete the expansion of $(w + x)^{6}$. $w^{6}+\square w^{5}x + 15w^{4}x^{2}+20w^{3}x^{3}+\square w^{2}x^{4}+6wx^{5}+x^{6}$

Explanation:

Step1: Recall Pascal's Triangle

Pascal's Triangle row for power \(n = 6\) is \(1,6,15,20,15,6,1\).

Step2: Match coefficients

For \((a + b)^n=\sum_{k = 0}^{n}\binom{n}{k}a^{n - k}b^{k}\), in \((w+x)^6\), when \(k = 1\) (term \(w^{5}x\)), coefficient is \(6\); when \(k=4\) (term \(w^{2}x^{4}\)), coefficient is \(15\).

Answer:

The first blank is \(6\), the second blank is \(15\).