Monomiaali

A monomiaali is a fundamental algebraic expression consisting of a single term. This term is formed by multiplying numbers and variables together. The numbers are called coefficients, and the variables are raised to non-negative integer powers. For instance, 5x²y³ is a monomiaali where 5 is the coefficient, x and y are variables, and 2 and 3 are their respective powers.

Monomiaali do not include addition or subtraction of terms. Expressions like 3x + 4y or 7a² - 2b are not monomiaali because they contain more than one term. The variables in a monomiaali must have non-negative integer exponents. Terms like 2/√x or 5x⁻¹ are not considered monomiaali in standard algebra.

Two monomiaali are considered like terms if they have the exact same variables raised to the exact same powers. For example, 7x²y and -3x²y are like terms. Expressions like 7x²y and 7xy² are not like terms because the powers of the variables differ. Like terms can be combined by adding or subtracting their coefficients. For example, 7x²y + (-3x²y) = 4x²y.

Monomiaali play a crucial role in forming polynomials, which are sums or differences of monomiaali. Operations such as multiplication and division of monomiaali are also fundamental algebraic skills, forming the basis for simplifying more complex expressions.