SSC (English Medium) Class 8Maharashtra State Board
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# Simplify: (A + B)3 − A3 − B3 - SSC (English Medium) Class 8 - Mathematics

Simplify:

(a + b)− a− b3

#### Solution

It is known that,

$a^3 - b^3 = \left( a - b \right)\left( a^2 + b^2 + ab \right)$

$\left( 3 \right) \left( a + b \right)^3 - a^3 - b^3$

$= \left( a + b \right)^3 - \left( a^3 + b^3 \right)$

$= \left( a + b \right)^3 - \left\{ \left( a + b \right)\left( a^2 + b^2 - ab \right) \right\}$

$= \left( a + b \right)\left\{ \left( a + b \right)^2 - \left( a^2 + b^2 - ab \right) \right\}$

$= \left( a + b \right)\left( a^2 + b^2 + 2ab - a^2 - b^2 + ab \right)$

$= \left( a + b \right)\left( 3ab \right)$

$= 3 a^2 b + 3a b^2$

Is there an error in this question or solution?

#### APPEARS IN

Balbharati Solution for Balbharati Class 8 Mathematics (2019 to Current)
Chapter 6: Factorisation of Algebraic expressions
Practice Set 6.3 | Q: 2.3 | Page no. 32
Solution Simplify: (A + B)3 − A3 − B3 Concept: Factors of A3 - B3.
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