Write the binomial expansion of the expression.
-$( a - b ) ^ { 6 }$
A) $a ^ { 6 } - 6 a ^ { 5 } b - 15 a ^ { 4 } b ^ { 2 } - 20 a ^ { 3 } b ^ { 3 } - 15 a ^ { 2 } b ^ { 4 } - 6 a b ^ { 5 } - b ^ { 6 }$
B) $a^{ 6} - 6 a ^ { 5 } b + 15 a ^ { 4 } b ^ { 2 } - 20 a ^ { 3 } b ^ { 3 } + 15 a ^ { 2 } b ^ { 4 } - 6 a b ^ { 5 } + b ^ { 6 }$
C) $a ^ { 6 } + 6 a ^ { 5 } b + 15 a ^ { 4 } b ^ { 2 } + 20 a ^ { 3 } b ^ { 3 } + 15 a ^ { 2 } b ^ { 4 } + 6 a b ^ { 5 } + b ^ { 6 }$
D) $- a ^ { 6 } + 6 a ^ { 5 } b - 15 a ^ { 4 } b ^ { 2 } + 20 a ^ { 3 } b ^ { 3 } - 15 a ^ { 2 } b ^ { 4 } + 6 a b ^ { 5 } - b ^ { 6 }$

Question

Quizplus · Accepted Answer

The correct expansion of $(a - b)^6$ involves alternating signs starting with a positive sign for $a^6$. The coefficients follow Pascal's triangle, which for the 6th row are 1, 6, 15, 20, 15, 6, 1, correctly applied in option B.

Write the Binomial Expansion of the Expression (a−b)6( a - b ) ^ { 6 }(a−b)6

Write the Binomial Expansion of the Expression $( a - b ) ^ { 6 }$