You also often cancel terms in a fraction when you know ( or assume) they are not zero.Fascheue said:What exactly does it mean to simplify an expression. I understand that an expression becomes more simple when you combine like terms but what other conditions are there? Is x(5x+1) more or less simple than 5x^2 +x? Do square roots need to be moved to the numerator?
Do these compiler contain optimizers in the way SQL Server does? Optimizer in SQL Server looks at query format, usage statistics, indexes and decides on best way of running query. Would be nice to have similar for other software.eys_physics said:As a side note, from the point of view of evaluating the expression numerically (on a computer) the first expression might be better. The reason is that the first one requires 4 operations (2 multiplications and 1 addition) but the second one 5 (3 multiplications and 1 addition). Many compilers are doing this kind of optimizations but it could have importance for script languages, if this sort of expressions are evaluated many times.
It's like art -- you know it when you see it.mfb said:It is not always unambiguous which expression is the easiest, but typically there are not many options.
Simplifying an expression means to manipulate it in such a way that it is written in its most compact and simplest form. This typically involves combining like terms, removing parentheses, and reducing fractions to their lowest terms.
Simplifying expressions can make them easier to understand and work with. It also allows us to find equivalent expressions that may be more useful in solving a problem or simplifying a larger equation.
The steps for simplifying an expression may vary depending on the specific expression, but generally involve removing parentheses, combining like terms, and reducing fractions. It is also important to follow the order of operations, simplifying expressions within parentheses first, then exponents, then multiplication and division from left to right, and finally addition and subtraction from left to right.
No, not all expressions can be simplified. Some expressions may already be in their simplest form, while others may not have any like terms to combine or any other simplification rules to apply.
Yes, there are several strategies for simplifying complex expressions. One is to break the expression down into smaller parts and simplify each part individually before combining them back together. Another is to look for patterns or common factors that can be factored out. Practice and familiarity with algebraic rules and techniques can also help in simplifying complex expressions.