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Simplify: A2b2(A + 2b)(3a + B) - Mathematics

Answer in Brief

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 \[3 a^4 b^2 + 7 a^3 b^3 + 2 a^2 b^4\] .

Concept: Multiplication of Algebraic Expressions
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APPEARS IN

RD Sharma Class 8 Maths
Chapter 6 Algebraic Expressions and Identities
Exercise 6.5 | Q 22 | Page 31
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