Final answer:
The verbal expression matching 4(2+2) is 'Four times the sum of two and two', demonstrating the associative property of addition. Factorials and systematic approaches help us understand combinations, while equating expressions is crucial in solving advanced mathematical problems.
Step-by-step explanation:
The verbal expression that matches the mathematical expression 4(2+2) is 'Four times the sum of two and two'. This phrase correctly describes the process of first adding two and two together to get a sum, and then multiplying that sum by four. The property that allows us to add two plus two before multiplying is known as the associative property of addition, which states that the grouping of the numbers does not affect the outcome of their addition, such as A + B is always equal to B + A.
When looking at combinations and permutations, as in the example where we might count the different ways to arrange four objects, using factorials like 4! (which equals 4 times 3 times 2 times 1) helps us understand the number of possible combinations. It's through orderly and systematic approaches that we can comprehend these mathematical concepts.
In arising problems, especially in physics or advanced mathematics, we can use equate different expressions to find a relationship between variables, as when we equate c^2 with an expression squared to solve for unknown quantities within an equation. This method encompasses both algebraic manipulation and understanding of formulas. Thus, the individual words or numbers work together in an equation in a somewhat similar way to how factors multiply together to achieve a final product in a factorial.