polynomial multiplaction quick

Answer 1

To multiply two polynomials quickly, follow these steps:

1. Write down the two polynomials in standard form, with the highest degree term first and descending order.

2. Multiply each term in the first polynomial by each term in the second polynomial.

3. Add together all the resulting terms, grouping like terms.

4. Simplify by combining like terms and rearranging if necessary.

Here's an example to illustrate the process:

Polynomial 1: 3x^2 + 2x + 1
Polynomial 2: 2x + 5

Multiply each term:
(3x^2)(2x) + (3x^2)(5) + (2x)(2x) + (2x)(5) + (1)(2x) + (1)(5)

Simplify and combine like terms:
6x^3 + 15x^2 + 4x^2 + 10x + 2x + 5

Combine like terms:
6x^3 + 19x^2 + 12x + 5

So the product of the two polynomials is 6x^3 + 19x^2 + 12x + 5.