Short Answer 6. Use Pascal's triangle to expand (3x-2)^6

## Step 1: Identify the Coefficients Using Pascal's Triangle<br />### For the expansion of $(a + b)^n$, use row $n$ of Pascal's Triangle. Here, $n = 6$. The coefficients are from row 6: $1, 6, 15, 20, 15, 6, 1$.<br />## Step 2: Apply the Binomial Expansion Formula<br />### Use the formula $(a + b)^n = \sum_{k=0}^{n} {n \choose k} a^{n-k} b^k$. Substitute $a = 3x$, $b = -2$, and $n = 6$.<br />## Step 3: Calculate Each Term<br />### Compute each term using the coefficients and powers of $a$ and $b$: <br />- First term: $1 \cdot (3x)^6 \cdot (-2)^0 = 729x^6$<br />- Second term: $6 \cdot (3x)^5 \cdot (-2)^1 = -1458x^5$<br />- Third term: $15 \cdot (3x)^4 \cdot (-2)^2 = 9720x^4$<br />- Fourth term: $20 \cdot (3x)^3 \cdot (-2)^3 = -25920x^3$<br />- Fifth term: $15 \cdot (3x)^2 \cdot (-2)^4 = 34560x^2$<br />- Sixth term: $6 \cdot (3x)^1 \cdot (-2)^5 = -15552x$<br />- Seventh term: $1 \cdot (3x)^0 \cdot (-2)^6 = 4096$<br /><br />## Step 4: Combine All Terms<br />### Sum all the terms to get the expanded form: <br />\[ 729x^6 - 1458x^5 + 9720x^4 - 25920x^3 + 34560x^2 - 15552x + 4096 \]