Use Pascal's triangle to expand the binomial.
-$( c + d ) ^ { 6 }$
A) $c ^ { 6 } + 6 c ^ { 5 } d + 15 c ^ { 4 } d ^ { 2 } + 20 c ^ { 3 } d ^ { 3 } + 15 c ^ { 2 } d ^ { 4 } + 6 c d ^ { 5 } + d ^ { 6 }$
B) $c ^ { 6 } + c ^ { 5 } d + c ^ { 4 } d ^ { 2 } + c ^ { 3 } d ^ { 3 } + c ^ { 2 } d ^ { 4 } + c d ^ { 5 } + d ^ { 6 }$
C) $c ^ { 6 } + d ^ { 6 }$
D) $c ^ { 6 } + 7 c ^ { 5 } d + 21 c ^ { 4 } d ^ { 2 } + 35 c ^ { 3 } d ^ { 3 } + 35 c d + 21 c ^ { 2 } d ^ { 4 } + 7 c d ^ { 5 } + d ^ { 6 }$

Question

Quizplus · Accepted Answer

Pascal's triangle provides the coefficients for each term in the expansion of a binomial expression. The 6th row of Pascal's triangle is 1, 6, 15, 20, 15, 6, 1, which matches the coefficients in option A for the expansion of $(c + d)^6$.

Use Pascal's Triangle to Expand the Binomial (c+d)6( c + d ) ^ { 6 }(c+d)6

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