Use Pascal's triangle to expand the binomial.
-$$( c - x ) ^ { 6 }$$
A) $c ^ { 6 } - 8 c ^ { 5 } x + 17 c ^ { 4 } x ^ { 2 } - 22 c ^ { 3 } x ^ { 3 } + 17 c ^ { 2 } x ^ { 4 } - 8 c x ^ { 5 } + x ^ { 6 }$
B) $c ^ { 6 } - 6 c ^ { 5 } x - 30 c ^ { 4 } x ^ { 2 } + 120 c ^ { 3 } x ^ { 3 } + 360 c ^ { 2 } x ^ { 4 } - 720 c x ^ { 5 } - 720 x ^ { 6 }$
C) $c ^ { 6 } - x ^ { 6 }$
D) $c ^ { 6 } - 6 c ^ { 5 } x + 15 c ^ { 4 } x ^ { 2 } - 20 c ^ { 3 } x ^ { 3 } + 15 c ^ { 2 } x ^ { 4 } - 6 c x ^ { 5 } + x ^ { 6 }$

Question

Quizplus · Accepted Answer

Pascal's triangle provides the coefficients for each term in the expansion of a binomial raised to a power. For $(c - x)^6$, the coefficients are 1, 6, 15, 20, 15, 6, 1, corresponding to each term from $c^6$ to $x^6$, with alternating signs starting with a positive for $c^6$.

Use Pascal's Triangle to Expand the Binomial (c−x)6( c - x ) ^ { 6 }(c−x)6

Use Pascal's Triangle to Expand the Binomial $( c - x ) ^ { 6 }$