Questions: Question 9 (Mandatory) (2 points) Divide. -14 a^2 b^3+21 a^3 b^2-28 a^4 b^4 / 7 a^2 b^2 -2 b+3 a^2-4 a b^2 -2 b+3 a^2 b-4 a^2 b^2 -2 b+3 a-4 a^2 b None of the above.

Solution Steps

To solve the given expression, we need to divide each term in the numerator by the denominator. This involves simplifying the expression by canceling out common factors in the numerator and the denominator.

1. Identify the common factors in the numerator and the denominator.
2. Divide each term in the numerator by the denominator.
3. Simplify the resulting expression.

We start with the expression to be divided: \[ \frac{-14 a^{2} b^{3}+21 a^{3} b^{2}-28 a^{4} b^{4}}{7 a^{2} b^{2}} \]

The numerator can be rewritten as: \[ -28 a^{4} b^{4} + 21 a^{3} b^{2} - 14 a^{2} b^{3} \]

Now, we divide each term in the numerator by the denominator \(7 a^{2} b^{2}\): \[ \frac{-28 a^{4} b^{4}}{7 a^{2} b^{2}} + \frac{21 a^{3} b^{2}}{7 a^{2} b^{2}} - \frac{14 a^{2} b^{3}}{7 a^{2} b^{2}} \]

Calculating each term gives: \[ -4 a^{2} b^{2} + 3 a - 2 b \]

Final Answer