A polynomial is an algebraic expression composed of variables and constants combined using addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are a foundational concept in algebra and higher mathematics.
\[ (a + b + c)x = ax + bx + cx \]
This identity shows how a monomial multiplies across the terms inside a parenthesis using the distributive property.
\[ (a + b)(m + n) = a(m + n) + b(m + n) \]
\[ = am + an + bm + bn \]
This is a standard polynomial expansion. Each term in the first binomial is multiplied by each term in the second.
\[ \frac{a + b + c}{x} = \frac{a}{x} + \frac{b}{x} + \frac{c}{x} \]
This demonstrates the rule for distributing a denominator across terms in the numerator.