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No.

A counter-example proves the falsity:

Consider the two binomials (x + 2) and (x - 2). Then

(x + 2)(x - 2) = x2 - 2x + 2x - 4

= x2 - 4

another binomial.

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Q: Will the product of two binomials after combining like terms always be trinomial?
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This is related to the fact that the square of both a positive and a negative number is always positive. The last term is simply the square of the second term, in the original binomial.


The product of a number and its reciprocal is always what?

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That is false. The product of two negative integers is always positive.


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