Question

unit 7 review assignment
topic 2: simplifying polynomials

1. \\(\frac{30a^6b^3 + 12a^4b^2 - 15a^2b}{3a^2b}\\)

Explanation:

Step1: Split the fraction

Split the numerator into three separate fractions over the same denominator: $\frac{30a^{6}b^{3}}{3a^{2}b} + \frac{12a^{4}b^{2}}{3a^{2}b} - \frac{15a^{2}b}{3a^{2}b}$

Step2: Simplify each fraction

• For the first fraction: $\frac{30}{3}a^{6 - 2}b^{3 - 1} = 10a^{4}b^{2}$
• For the second fraction: $\frac{12}{3}a^{4 - 2}b^{2 - 1} = 4a^{2}b$
• For the third fraction: $\frac{15}{3}a^{2 - 2}b^{1 - 1} = 5a^{0}b^{0} = 5$ (since $a^{0}=1$ and $b^{0}=1$)

Step3: Combine the simplified terms

Combine the results from Step 2: $10a^{4}b^{2} + 4a^{2}b - 5$

Answer:

$10a^{4}b^{2} + 4a^{2}b - 5$