Question

How do you expand `(3a-b)^4` using Pascal’s Triangle?

Answer 1

`81a^4-108a^3b+54a^2b^2-12ab^3+b^4`

Explanation:

from pascal's triangle we can see,

`(1+x)^0`---------------------`1`
`(1+x)^1`---------------------`1` `1`
`(1+x)^2`--------------------`1` `2` `1`
`(1+x)^3`--------------------`1` `3` `3` `1`
`(1+x)^4`--------------------`1` `4` `6` `4` `1`

so,
`(3a-b)^4=1*(3a)^4-4*(3a)^3b+6*(3a)^2b^2-4*3ab^3+1*b^4`
`=81a^4-108a^3b+54a^2b^2-12ab^3+b^4`