Bird Li
03/22/2024 · Junior High School
Factor out the greatest common factor from the following polynomial. \( 36 a^{3} b^{3}-27 a^{6} b^{6}+27 a b-36 a^{6} b \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( 36 a^{3} b^{3}-27 a^{6} b^{6}+27 a b-36 a^{6} b= \) (Type your answer in factored form.) B. The polynomial has no common factor other than 1 .
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
Factor the expression \( 36a^3b^3-27a^6b^6+27ab-36a^6b \).
Factor the expression by following steps:
- step0: Factor:
\(36a^{3}b^{3}-27a^{6}b^{6}+27ab-36a^{6}b\)
- step1: Factor the expression:
\(9\left(4a^{3}b^{3}-3a^{6}b^{6}+3ab-4a^{6}b\right)\)
- step2: Factor the expression:
\(9ab\left(4a^{2}b^{2}-3a^{5}b^{5}+3-4a^{5}\right)\)
The factored form of the polynomial \(36a^{3}b^{3}-27a^{6}b^{6}+27ab-36a^{6}b\) is \(9ab(4a^{2}b^{2}-3a^{5}b^{5}+3-4a^{5})\).
Therefore, the correct choice is:
A. \(36a^{3}b^{3}-27a^{6}b^{6}+27ab-36a^{6}b = 9ab(4a^{2}b^{2}-3a^{5}b^{5}+3-4a^{5})\)
Quick Answer
A. \(36a^{3}b^{3}-27a^{6}b^{6}+27ab-36a^{6}b = 9ab(4a^{2}b^{2}-3a^{5}b^{5}+3-4a^{5})\)
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