ab×dc

ab×dc is an expression that can be read in more than one way, depending on the mathematical context. In basic algebra, if a, b, c, and d are scalars, ab×dc denotes the product of the two monomials ab and dc. Because real and complex multiplication is associative and commutative, this equals a b d c, and the four factors can be rearranged in any order (for example, ad×bc or ac×bd) without changing the value.

In vector algebra, the symbol × is commonly used for the cross product of two vectors in three-dimensional space. If ab and dc were to be interpreted as vectors, then ab×dc would mean the cross product of those two vectors. However, ab and dc are not standard vector names; typically vectors are denoted by letters such as u and v, written plainly as u×v. The cross product u×v yields a vector perpendicular to the plane containing u and v, with magnitude |u||v|sinθ and direction given by the right-hand rule. The cross product is anti-commutative, so u×v = −(v×u).

If a, b, c, d are matrices or polynomials, the expression ab×dc would require explicit definition of the operations involved, since the cross product is not defined for arbitrary matrices or scalars. In such cases, one would usually perform the scalar parts first (ab and dc) and then apply the cross product only if the results are vectors.

Example: with scalars a=2, b=3, d=5, c=4, ab×dc = (2·3) × (5·4) = 6×20 = 120.