Question

Using pascal triangle solve (x+2y)4?

`(x+2y)^4`

Answer 1

Use the 4th row of pascal triangle.*

Explanation:

Remember how the Pascal triangle looks.

We start at the top: write 3 one in a triangle shape, then sum each two numbers of previous line.
1
1 1
1 (1+1) 1
1 (1+2) (1+2) 1

The 4th row is: `1` `4` `6` `4` `1`
* numeration of rows *
This numbers are binomial coefficient:
`(a+b)^4=color(red)(1) a^4+color(red)(4)a^3 b+color(red)(6)a^2 b^2 +color(red)(4)a b^3+color(red)(1)b^4`
in your case: `a=x, b=2y`
`(x+2 y)^4=color(red)(1) x^4+color(red)(4)x^3 2 y+color(red)(6)x^2 (2 y)^2 +color(red)(4)x (2y)^3+color(red)(1)(2y)^4=`
`= x^4+8 x^3 y+24 x^2 y^2 +32 x y^3+16 y^4`