Expand the binomial.
-$( p - q ) ^ { 6 }$
A) $p ^ { 6 } - q ^ { 6 }$
B) $\mathrm { p } ^ { 6 } - 8 \mathrm { p } ^ { 5 } \mathrm { q } + 17 \mathrm { p } ^ { 4 } \mathrm { q } ^ { 2 } - 22 \mathrm { p } ^ { 3 } \mathrm { q } ^ { 3 } + 17 \mathrm { p } ^ { 2 } \mathrm { q } ^ { 4 } - 8 \mathrm { pq } ^ { 5 } + \mathrm { q } ^ { 6 }$
C) $p ^ { 6 } - 6 p ^ { 5 } q - 30 p ^ { 4 } q ^ { 2 } + 120 p ^ { 3 } q ^ { 3 } + 360 p ^ { 2 } q ^ { 4 } - 720 p q ^ { 5 } - 720 q ^ { 6 }$
D) $p ^ { 6 } - 6 p ^ { 5 } q + 15 p ^ { 4 } q ^ { 2 } - 20 p ^ { 3 } q ^ { 3 } + 15 p ^ { 2 } q ^ { 4 } - 6 p q ^ { 5 } + q ^ { 6 }$

Question

Quizplus · Accepted Answer

The correct expansion of $( p - q ) ^ { 6 }$ uses the binomial theorem, which involves combinations and powers of both terms. The coefficients follow Pascal's triangle, and for the 6th power, they are 1, 6, 15, 20, 15, 6, 1, correctly reflected in option D.

Expand the Binomial (p−q)6( p - q ) ^ { 6 }(p−q)6

Expand the Binomial $( p - q ) ^ { 6 }$