Question

How do you multiply `(x+7)^4`?

Answer 1

`x^4 + 28x^3 + 294x^2 + 1372x + 2401`

Explanation:

Using the first 5 rows of Pascal's Triangle:
#{: (0, ":", 1,,,,), (1, ":", 1, 1,,,), (2,":", 1,2, 1,,), (3,":",1,3,3,1,), (4,":",1,4,6,4,1) :}#

`(a+b)^4 = 1a^4b^0+4a^3b^1+6a^2b^2+4a^1b^3+1a^0b^4`

Substituting `x` for `a` and `7` for `b`

`(x+7)^4`
`color(white)("XXXX")` `= x^4 + 4x^3(7^1)+6x^2(7^2)+4x(7^3) + 1(7^4)`

`color(white)("XXXX")` `=x^4 + 28x^3 + 294x^2 + 1372x + 2401`