Math Problem Statement
simplify: 2[9(A-B) + 7(2B-A)] - 2[3(2B+A) - 2(A+3B) - 5(A+B)]
Solution
Let's simplify the given expression step by step:
The expression is:
[ 2[9(A-B) + 7(2B - A)] - 2[3(2B + A) - 2(A + 3B) - 5(A + B)] ]
Step 1: Simplify inside the first bracket
Expand the terms inside the first set of brackets: Now, combine these: Thus, the first bracket becomes:
Step 2: Simplify inside the second bracket
Expand the terms inside the second set of brackets: Now, combine these: Thus, the second bracket becomes:
Step 3: Apply the factors outside the brackets
Now multiply the factors outside the brackets:
Step 4: Combine the results
Now combine the two results:
Thus, the simplified expression is:
Would you like further clarification on any part of this solution?
Here are five related questions to extend your understanding:
- How would you simplify a similar expression with three variables?
- What is the distributive property, and how does it apply in this case?
- Can this result be factored? If so, how?
- What is the general approach to simplify expressions involving nested brackets?
- How would the expression change if the sign of one of the terms inside the brackets were different?
Tip: Always simplify inside the brackets first, then apply the multiplication outside the brackets step by step.
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Math Problem Analysis
Mathematical Concepts
Algebra
Simplification
Distributive Property
Formulas
Distributive Property: a(b + c) = ab + ac
Theorems
Distributive Property
Suitable Grade Level
Grades 8-10
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