9(4(2n+r)-11r)+3(r-n)

9 ( 4 ( 2n + r ) - 11r ) + 3 ( r - n )

Work from the innermost parentheses first: Solve 4 ( 2n + r ) by using the distributive property:

    4 ( 2n + r  ) =  4 x 2n + 4 x r   =   8n + 4r

This gives us:   9 ( 8n + 4r - 11r ) + 3 ( r - n )

Still working inside the first set of parentheses, combine   4r   with   - 11r   to give   - 7r.

We now have:   9 ( 8n - 7r ) + 3 ( r - n ).

Now use the distributive property on both sets of parentheses:

    9 ( 8n - 7r )   =  9 x 8n  -  9 x 7r   =   72n - 63r                         3 ( r - n )   =  3 x r  -  3 x n   =   3r - 3n

This becomes:   72n - 63r + 3r - 3n

Which is:   69n - 60r