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Which is true about the completely simplified difference of the polynomials a3b + 9a2b2 − 4ab5 and a3b − 3a2b2 + ab5?
The difference is a binomial with a degree of 5.
The difference is a binomial with a degree of 6.
The difference is a trinomial with a degree of 5.
The difference is a trinomial with a degree of 6.
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Compute the difference:
(a^3b + 9a^2b^2 − 4ab^5) − (a^3b − 3a^2b^2 + ab^5)
= a^3b − a^3b + 9a^2b^2 − (−3a^2b^2) − 4ab^5 − ab^5
= 12a^2b^2 − 5ab^5.
This is a binomial. Degrees: 12a^2b^2 has degree 4, −5ab^5 has degree 6, so the polynomial’s degree is 6.
Answer: The difference is a binomial with a degree of 6.
(a^3b + 9a^2b^2 − 4ab^5) − (a^3b − 3a^2b^2 + ab^5)
= a^3b − a^3b + 9a^2b^2 − (−3a^2b^2) − 4ab^5 − ab^5
= 12a^2b^2 − 5ab^5.
This is a binomial. Degrees: 12a^2b^2 has degree 4, −5ab^5 has degree 6, so the polynomial’s degree is 6.
Answer: The difference is a binomial with a degree of 6.
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