Simplify the following expression.‐3 + 7(a – 3b – 1) – 4(10 – a + 2b)11a - 11b - 4411a - 29b - 503a - 13b - 506a - b - 44

1. Break Down the Problem

We need to simplify the given expression:
$-3 + 7(a - 3b - 1) - 4(10 - a + 2b)$ followed by $11a - 11b - 44$ and other similar expressions.

2. Relevant Concepts

We will apply the distributive property to expand the terms and then combine like terms. The distributive property states that $a(b + c) = ab + ac$.

3. Analysis and Detail

Let's simplify the expression step-by-step:

1. Expand the expressions:

   • First term: $7(a - 3b - 1) = 7a - 21b - 7$
   • Second term: $-4(10 - a + 2b) = -40 + 4a - 8b$

2. Combine the terms: $-3 + (7a - 21b - 7) + (-40 + 4a - 8b)$ Combining the constant terms and coefficients of $a$ and $b$: $(-3 - 7 - 40) + (7a + 4a) + (-21b - 8b)$ which simplifies to: $-50 + 11a - 29b$

3. Add the remaining expressions: Combine our result with $11a - 11b - 44$: $(-50 + 11a - 29b) + (11a - 11b - 44)$ Again, combine like terms: $11a + 11a - 29b - 11b - 50 - 44$ This gives: $22a - 40b - 94$

4. Verify and Summarize

We’ve correctly expanded and combined the terms according to algebraic rules. All calculations have been verified at each step.

Final Answer

The final simplified expression is:
$22a - 40b - 94$