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.

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  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

step-by-step explanation:

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