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18 January, 15:33

Which is a counterexample that disproves the conjecture? After completing several multiplication problems, a student concludes that the product of two binomials is always a trinomial.

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  1. 18 January, 16:35
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    When you make the product of a binomial of the kind x + a times other binomial that is of the kind x - a, you obtain another binomial (not a trinomial), so any example with that form will be a counterexample that disproves the conjecture:

    (x + a) * (x - a) = x^2 - a^2

    For example, (x + 3) * (x - 3) = x^2 - 9. So, not always the product of two binomials is a trinomial.
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