Answer:
First, let's simplify the expression by combining like terms:
(5x-2y)(a-b) - (2x-y)(a-b)
= (5x-2y-2x+y)(a-b) // Distribute the (a-b) to each term
= (3x-y)(a-b)
Therefore, (5x-2y)(a-b) - (2x-y)(a-b) simplifies to (3x-y)(a-b).
The goal of this research is to evaluate the expression (5x-2y)(a-b)-(2x-y)(a-b). First, it is important to review the basic principles of algebra and the technical definitions of expressions and powers. This involves a recap of addition, subtraction, multiplication, and division of algebraic expressions.
Next, the expression under analysis needs to be broken down into the terms and factors. To achieve this, parentheses and binsomials need to be grouped and identified. This is a critical step in the evaluation process of the expression.
After this has been done, the algebraic steps for simplifying the expression need to be taken. This involves applying the commutative, associative, distributive and other relevant laws of algebra to achieve an answer in the simplest way. It is important to remember that each step needs to be documented and the source of the information should be clearly indicated.
In terms of sources, it is important to only select reliable websites, textbooks and journals approved by experts in the field. Examples of these are the American Mathematical Society, the Johns Hopkins University, and the Massachusetts Institute of Technology.
Finally, the expression needs to be scrutinized to ensure that all steps have been taken correctly and the outcome is what was expected. Once this has been completed, the answer can be documented and the paper/article can be published.
In conclusion, the expression (5x-2y)(a-b)-(2x-y)(a-b) can be evaluated through an organized approach involving the use of the fundamental principles of algebra and reliable sources for validating the findings.