Write a statement about how many terms you will get when you multiply a polynomial with m terms by a polynomial with n terms. Give an explanation to support your statement.

9514 1404 393

  The initial product will have mn terms, but simplification my reduce that number to as few as one or two terms.

Step-by-step explanation:

We have to assume each polynomial is in standard form. Each of the m terms of the first polynomial will be multiplied by each of the n terms of the second, so there will be a total of m×n terms resulting from the initial multiplication.

Some of those terms may be combined when the sum is simplified, so the end result may have as few as 1 or 2 terms.

Examples:

1. 2 × b = 2b . . . . . each has 1 term; the result has 1 term.

2. (x -a)(x +a) = x² -ax +ax -a² (2×2=4 terms) = x² -a² . . . . the result has 2 terms.

3. (x -a)(x³ +x) = x⁴ -ax³ +x² -ax . . . the result has 2×2 = 4 terms

found it xd it ok yt