Multiplying a Monomial by a Trinomial
In algebra, multiplication involves not only multiplying numbers but also extending the method to algebraic expressions. A monomial is an expression containing a single term, while a trinomial contains three terms.
To multiply a monomial by a trinomial, we utilize the distributive law, which allows us to multiply each term in the trinomial by the monomial separately. For example, if we take a monomial such as 3p and multiply it by the trinomial 4p² + 5p + 7, we can break this down into:
$$
3p \times (4p² + 5p + 7) = (3p \times 4p²) + (3p \times 5p) + (3p \times 7)
$$
This results in:
12p³ from multiplying 3p and 4p²15p² from multiplying 3p and 5p21p from multiplying 3p and 7
The final outcome of this multiplication yields a polynomial: 12p³ + 15p² + 21p. This systematic approach not only simplifies the process of multiplying complex expressions but also sets the foundation for polynomial algebra, making further expressions easier to handle. In summary, mastering this technique is vital for solving more advanced algebraic expressions.