Question

Which is true about the completely simplified difference of the polynomials a3b 9a2b2 − 4ab5 and a3b − 3a2b2 ab5?.

Answer 1

The simplified difference of the polynomials (a³b+9a²b²-4ab⁵) and (a³b-3a²b²+ab⁵) is (12a²b²-5ab⁵).

What are Like terms?

Like terms are those terms that are having the same variables, also the variables are of the same order as well.

for example, 25x and 5x are like terms; 30xy and 7xy are like terms, 9x³ and 4x² are not like terms, etc.

Let's simplify the two of the given polynomials, therefore, find the difference between the two given polynomials.

$a^3b+9a^2b^2 - 4ab^5 - (a^3b - 3a^2b^2+ab^5)\\\\= a^3b+9a^2b^2 - 4ab^5 - a^3b + 3a^2b^2-ab^5\\\\\text{Bring Like terms together}\\\\=a^3b - a^3b+9a^2b^2+3a^2b^2 -4ab^5-ab^5\\\\= 12a^2b^2-5ab^5$

Hence, the simplified difference of the polynomials (a³b+9a²b²-4ab⁵) and (a³b-3a²b²+ab⁵) is (12a²b²-5ab⁵).

Learn more about Like Terms:

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