Simplifying Polynomial Functions

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Simplify the following polynomial function:

$ab^{-2}(a^{2}b + a^{-1}b^{3}-a^{3}b^{-1})$

$\frac{a^{3}}{b}+b-\frac{a^{4}}{b^{3}}$

CORRECT

$\frac{a^{3}}{b}-\frac{a^{4}}{b^{3}}$

$\frac{a^{3}}{b}+\frac{a^{4}}{b^{3}}$

$\frac{a^{3}}{b}+b^{2}-\frac{a^{4}}{b^{3}}$

$\frac{a^{3}}{b}-b+\frac{a^{4}}{b^{3}}$

First, multiply the outside term with each term within the parentheses:

$ab^{-2}(a^{2}b + a^{-1}b^{3}-a^{3}b^{-1})$

$a^{3}b^{-1} + b-a^{4}b^{-3}$

Rearranging the polynomial into fractional form, we get:

$\frac{a^{3}}{b}+b-\frac{a^{4}}{b^{3}}$

Simplify the following polynomial:

$(\frac{-a^{-2}b^{3}c^{-1}}{3a^{-4}b^{-1}c^{3}})^{-2}$

$\frac{9c^{8}}{a^{4}b^{8}}$

CORRECT

$\frac{c^{8}}{9a^{4}b^{8}}$

$\frac{9a^{4}}{c^{8}b^{8}}$

$\frac{9b^{8}}{c^{8}a^{4}}$

$\frac{9a^{4}}{c^{8}b^{4}}$

To simplify the polynomial, begin by combining like terms:

$(\frac{-a^{-2}b^{3}c^{-1}}{3a^{-4}b^{-1}c^{3}})^{-2}$

$(\frac{-a^{2}b^{4}}{3c^{4}})^{-2}$