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Question
Simplify:
a2b2(a + 2b)(3a + b)
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Solution
To simplify, we will proceed as follows:
\[a^2 b^2 \left( a + 2b \right)\left( 3a + b \right)\]
\[ = \left[ a^2 b^2 \left( a + 2b \right) \right]\left( 3a + b \right)\]
\[ = \left( a^3 b^2 + 2 a^2 b^3 \right)\left( 3a + b \right)\]
\[ = 3a\left( a^3 b^2 + 2 a^2 b^3 \right) + b\left( a^3 b^2 + 2 a^2 b^3 \right)\]
\[ = 3 a^4 b^2 + 6 a^3 b^3 + a^3 b^3 + 2 a^2 b^4 \]
\[ = 3 a^4 b^2 + 7 a^3 b^3 + 2 a^2 b^4\]
Thus, the answer is \[3 a^4 b^2 + 7 a^3 b^3 + 2 a^2 b^4\] .
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