Xavier said the product of a monomial and a binomial will always be a trinomial. Explain the error in his reasoning.
2 answers:
All that is needed is a single counter-example.
One counter-example is to multiply the monomial x^3 with the binomial x^7-10x^4
We then get...
x^3*(x^7-10x^4) = x^3*x^7 + x^3*(-10x^4)
x^3*(x^7-10x^4) = x^10 - x^7
The result we get is a binomial as there are still only two terms here. We would need three terms to have a trinomial.
Answer:
See below.
Step-by-step explanation:
Each term in the binomial ( there are 2 terms, by definition) is multiplied by the single term (monomial) so the answer will be another binomial.
For example:
2x (x - 6)
= 2x^2 - 12x.
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