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You asked about simplifying -21(a+2b)+14a-9b.
The important thing to remember is that you can add apples to apples and oranges to oranges, but you can't add (or subtract) apples to oranges. In algebra, the types of fruit are the variable names like a and b in your expression.
I'm going to show you how to solve a slightly changed problem:
Simplify 4x - 9( y - 3x) - 8 + 10y.
First multiply through by -9 to remove the parentheses:
4x - 9y + 27x - 8 + 10y
Now group "like" terms. That means you can add the terms (the terms are the things between the pluses and minuses) together that have the same variables only. So 4x and - 27x are like terms. And -9y and 10y are like terms. So that means
(4x + 27x) + (-9y + 10y) - 8
31x + y - 8.
Each of these three terms has no other "like" terms, so this is simplified.
You can solve your expression using the same steps I've shown you here.
Hope this helps,
Stephen La Rocque.