Use Pascal's triangle to expand the binomial.
-$( p + q ) ^ { 5 }$
A) $\mathrm { p } ^ { 5 } + \mathrm { p } ^ { 4 } \mathrm { q } + \mathrm { p } ^ { 3 } \mathrm { q } ^ { 2 } + \mathrm { p } ^ { 2 } \mathrm { q } ^ { 3 } + \mathrm { pq } + \mathrm { q } ^ { 5 }$
B) $\mathrm { p } ^ { 5 } + 5 \mathrm { p } ^ { 4 } \mathrm { q } + 10 \mathrm { p } ^ { 3 } \mathrm { q } ^ { 2 } + 10 \mathrm { p } ^ { 2 } \mathrm { q } ^ { 3 } + 5 \mathrm { pq } \mathrm { q } ^ { 4 } + \mathrm { q } ^ { 5 }$
C) $\mathrm { p } ^ { 5 } + 6 \mathrm { p } ^ { 4 } \mathrm { q } + 15 \mathrm { p } ^ { 3 } \mathrm { q } ^ { 2 } + 20 \mathrm { p } ^ { 3 } \mathrm { q } ^ { 3 } + 15 \mathrm { p } ^ { 2 } \mathrm { q } ^ { 3 } + 6 p \mathrm { q } ^ { 4 } + \mathrm { q } ^ { 5 }$
D) $p ^ { 5 } + q ^ { 5 }$

Question

Quizplus · Accepted Answer

Pascal's triangle provides the coefficients for the expansion of a binomial expression raised to a power. The 6th row (for $n=5$) is 1, 5, 10, 10, 5, 1, which matches the coefficients in option B for the expansion of $(p + q)^5$.

Use Pascal's Triangle to Expand the Binomial (p+q)5( p + q ) ^ { 5 }(p+q)5

Use Pascal's Triangle to Expand the Binomial $( p + q ) ^ { 5 }$