Math Problem Statement
(\sum_{i=4}^{6}(3-2x_{i}))^{2}-2\sum_{i=1}^{6}6x_{i}
Solution
Let's break down the expression step by step and solve it.
The given expression is:
Step 1: Evaluate the summation
This summation expands as:
So,
Step 2: Square the result
Step 3: Evaluate the summation
This summation expands as:
Step 4: Multiply the result by
Step 5: Combine all parts
The full expression now becomes:
This is the simplified form of the expression.
Would you like more details or further steps?
Related Questions:
- How do you expand and simplify a squared binomial like ?
- How would this expression change if the summation limits were different?
- What if there were additional terms inside the summation? How would it affect the final result?
- Can you factorize the expression ?
- How does the expression simplify if are specific numbers?
Tip:
When working with summations, always ensure to evaluate them carefully before moving on to further operations like squaring or multiplication.
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Math Problem Analysis
Mathematical Concepts
Summation
Binomial Expansion
Quadratic Equation
Formulas
Binomial expansion formula
Quadratic equation formula
Theorems
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Suitable Grade Level
Advanced High School
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