Final answer:
The question requires simplifying a given algebraic expression using algebraic rules such as expansion, combining like terms, and factoring. The simplification process involves correctly applying powers to terms within parentheses and potentially completing the square for certain expressions.
Step-by-step explanation:
The student's question concerns the simplification of a mathematical expression. This involves the use of algebraic rules to expand and then simplify the given expressions. The step-by-step approach should be taken to simplify the expressions correctly. For instance, when expanding the expression (2x)², one should recognize that it equals 4x², considering that squaring the term (2x) means squaring both the coefficient 2 and the variable x. Then, the simplification process involves possible factoring, canceling out terms, and combining like terms according to algebraic principles.
When dealing with the fraction (2-3)(x-3X2) / (4-2)(x4), it's crucial to first simplify the numerator and denominator before attempting to divide. By expanding and simplifying, you can find the simplest form of the expression. Note that each term within the parentheses is affected by the power outside and that any operations within the parentheses are performed before applying the power to them.
Remember, when completing the square with expressions such as x², the goal is to form a perfect square trinomial that can be factored into a binomial squared. Additionally, when simplifying equations involving exponents, applying the exponent to each term within the base is necessary.