Pascal 's triangle is
1
1,1
1,2,1
1,3,3,1
1,4,6,4,1
1,5,10,10,5,1 the row 1,5,10,10,5,1 is the one we need to expand (8v+s)⁵. Given (a+b)⁵ each term of the row is the coefficient of akbtwith k goes form 5 to 0 and t goes from 0 to 5. so (a+b)⁵=1a⁵b⁰+5a⁴b¹+10a³b²+10a²b³+5a¹b⁵+1a⁰b⁵=a⁵+5a⁴b+10a³b²+10a²b³+5ab⁵+b⁵. In the case of (8v+s)⁵: a=8v
b=s 1(8v)⁵s⁰+5(8v)⁴s¹+10(8v)³s²+10(8v)²s³+5(8v)¹s⁵+1(8v)⁰s⁵ = (8v)⁵+5(8v)⁴s+10(8v)³s²+10(8v)²s³+5(8v)s⁵+s⁵= = 8⁵v⁵+5⋅8⁴v⁴s+10⋅8³v³s²+10⋅8²v²s³+40vs⁵+s⁵= = 32768v⁵+20480v⁴s+5120v³s²+640v²s³+40vs⁵+s⁵.