Multiplying polynomials involves combining two or more polynomial expressions to get a new polynomial. A polynomial is an expression made up of variables and coefficients, connected by addition, subtraction, and multiplication.
To multiply polynomials, you typically use the distributive property, also known as the FOIL method for binomials, or you can apply the area model. Here’s a simple step-by-step approach:
- Multiply each term in the first polynomial by each term in the second polynomial: For example, if you want to multiply (2x + 3) and (x + 4), you would multiply 2x by both x and 4, and then multiply 3 by both x and 4.
- Combine like terms: After performing all the multiplications, combine any like terms to simplify your polynomial. In the previous example, you would end up with 2x² + 8x + 3x + 12, which simplifies to 2x² + 11x + 12.
In essence, multiplying polynomials is just a systematic way of applying the distributive property to multiply each term together and then simplifying the result. It’s a fundamental skill in algebra that builds the foundation for more advanced mathematical concepts.