Question

How do you expand `(4a^3+1)^4`?

Answer 1

`=256a^12+256a^9+96a^6+16a^3+1`

Explanation:

Using Pascal's triangle we can find the coefficients of the values in the bracket. Since our case is to the power of 4, we use the 4th row and we can see

• We will have coefficents
  `1, 4, 6, 4, 1`

So, if have a `(a+b)^4` it will equal
`1*a^4*b^0+4*a^3*b^1+6*a^2+b^2+4*a^1*b^3+1*a^0*b^4`

Then for our case, we expand like this:
`(4a^3+1)^4`
`=(4a^3)^4*1^0+4*(4a^3)^3*1^1+6*(4a^3)^2*1^2+4*(4a^3)^1*1^3+(4a^3)^0*1^4`

`=256a^12+256a^9+96a^6+16a^3+1`

I hope I didn't clumsy up my calculation, good luck :)