Use Pascal's triangle and the patterns explored to write the expansion. (a - b)⁶ A) a⁶ - 6a⁵b - 16a⁴b² - 22a³b³ - 16a²b⁴ - 6ab⁵ - b⁶ B) a⁶ - 6a⁵b + 16a⁴b² - 22a³b³ + 16a²b⁴ - 6ab⁵ + b⁶ C) a⁶ + 6a⁵b + 15a⁴b² + 20a³b³ + 15a²b⁴ + 6ab⁵ + b⁶ D) a⁶ - 6a⁵b + 15a⁴b² - 20a³b³ + 15a²b⁴ - 6ab⁵ + b⁶

Question

Quizplus · Accepted Answer

The correct expansion follows the pattern of Pascal's triangle for the binomial expansion of $(a - b)^n$, where $n=6$ in this case. The coefficients (1, -6, 15, -20, 15, -6, 1) match the 7th row of Pascal's triangle (considering the first row as row 0), and the signs alternate starting with a positive sign for $a^6$.

Use Pascal's Triangle and the Patterns Explored to Write the Expansion