Final answer:
The question involves algebra and vector calculations, requiring understanding of the distributive law, properties of the cross product, and equality principles. Expressions must be manipulated correctly to demonstrate equivalency or solve problems within the field of mathematics.
Step-by-step explanation:
Understanding Algebraic Expressions and Vector Products
The given student question involves recognizing and applying algebraic properties such as the distributive law to rearrange expressions correctly. In mathematics, particularly in algebra and vector calculus, it's essential to understand how to manipulate expressions to show equivalency or to solve for variables.
For instance, the distributive property is given as A(B + C) = AB + AC. This property allows us to multiply a single term by each term inside a parenthesis. Similarly, when working with vectors, the cross product, which is denoted by ×, has unique properties such as being anticommutative. This means that A × B is not the same as B × A; instead, it equals -(B × A). Furthermore, factoring is a method used to simplify expressions, for example, by grouping terms that contain a common unit vector.
When dealing with equations, it's vital to remember that multiplication or division by the same number on both sides does not change the equality. This principle is helpful when solving for variables. For vectors, scalar multiplication is used to describe vectors in different directions or magnitudes, such as the negative of a vector –Ă = –AxÎ + –AyÍ + –AzÎ.