ab×cd

ab×cd denotes the product of two terms, ab and cd, in algebra. Here a, b, c, and d are elements of a ring, field, or algebra in which multiplication is defined. The expression is typically read as (ab)(cd), the product of four factors in that specific order. Because multiplication is associative, the parentheses can be rearranged in a way that preserves order, so (ab)(cd) equals a(b(cd)) equals abcd.

In a commutative setting, the factors may be rearranged without changing the result. Therefore (ab)(cd) = (ac)(bd) = (ad)(bc) = abcd. In noncommutative contexts, such as certain matrix rings, you may not permute the factors freely, so (ab)(cd) is generally not the same as (ac)(bd) or other rearrangements even though it equals abcd in the written order.

If a, b, c, d are real or complex numbers, ab×cd evaluates to the single number abcd. If they are indeterminates or variables, ab×cd is the monomial abcd, a term of total degree 4. In polynomial multiplication, this expression arises when multiplying two monomials or binomials and simplifies by combining the factors in the same order.

Overall, ab×cd is a basic product of four factors that illustrates how multiplication distributes over addition, behaves under associativity, and, in commutative systems, allows straightforward rearrangement of factors. See also: multiplication in rings, distributive property, monomials.