2×ab

2×ab denotes twice the product of a and b. In standard notation this is written as 2ab and understood as the scalar 2 multiplied by the product ab. Because multiplication is associative and, for real or complex numbers, commutative, 2ab can be regrouped as (2a)b or a(2b) without changing the value.

In algebra, 2ab is a monomial term whose degree is the sum of the degrees of a and b when a and b are variables. It commonly appears in the expansion of (a+b)^2, where the middle term is 2ab. Geometrically, if ab represents the area of a rectangle with sides a and b, then 2ab is twice that area. In physics and other disciplines, 2ab often appears as a cross term representing interaction between quantities a and b.

Examples: if a = 3 and b = 4, then 2ab = 2 × 3 × 4 = 24. If a = −2 and b = 5, then 2ab = 2 × (−2) × 5 = −20. If a = b = t, then 2ab = 2t^2.

Special cases and notes: If either a or b is zero, 2ab = 0. If a and b are matrices or other objects, 2×ab represents scalar multiplication of the matrix product ab; the product ab must be defined (dimensions must be compatible) for the expression to be meaningful. In standard real-number arithmetic, 2ab can be interpreted equivalently as (2a)b or a(2b).