polynomial multiplaction quick
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.
To quickly multiply two polynomials, follow these steps:
1. Write down the two polynomials.
Let's say we have polynomial A(x) = 2x^2 + 3x + 1 and polynomial B(x) = 4x + 2.
2. Multiply each term of polynomial A(x) by each term of polynomial B(x).
Multiply 2x^2 by 4x, 2x^2 by 2, 3x by 4x, 3x by 2, 1 by 4x, and 1 by 2.
3. Simplify each multiplication result.
Multiply 2x^2 by 4x to get 8x^3, multiply 2x^2 by 2 to get 4x^2, multiply 3x by 4x to get 12x^2,
multiply 3x by 2 to get 6x, multiply 1 by 4x to get 4x, and multiply 1 by 2 to get 2.
4. Add all the simplified terms.
Combine like terms by adding up the terms with the same exponent. In our example, we have
8x^3 + 12x^2 + 6x + 4x + 2.
5. Write the final polynomial.
Rearrange the terms in descending order of exponents. In our example, the final polynomial is
8x^3 + 12x^2 + 10x + 2.
So, the product of the two polynomials is 8x^3 + 12x^2 + 10x + 2.