3×bc

3×bc is a mathematical expression representing the product of the constant 3 and the product of two variables, b and c. In standard notation it is written as 3bc, or as 3·b·c. Because multiplication is associative and commutative, the factors can be rearranged without changing the value: 3bc = bc3 = b(3c) = (3b)c.

As a monomial, 3bc has a coefficient of 3 and two variable factors, so it is a second-degree monomial in b and c. The total degree is 2, since the exponents of b and c sum to 2. It is a simple example of a polynomial term.

Usage in polynomials: 3bc can appear as a standalone term or as part of larger expressions. If combined with other terms sharing a common factor, that factor can be pulled out. For example, 3bc + 6bd = 3b(c+d); 3bc + 9ec = 3c(b+3e).

Numeric example: if b = 4 and c = 5, then 3×bc = 3×(4×5) = 60.

Context and variants: coefficients like 3 multiply products of variables in expansions, area calculations, or algebraic identities. The concept generalizes to rings and fields, where the coefficient 3 is interpreted within the underlying arithmetic structure and can be reduced modulo a characteristic if applicable.

See also: monomial, polynomial, coefficient, factoring, distributive property.