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Simplify: P3 − (P + 1)3 - SSC (English Medium) Class 8 - Mathematics

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Question

Simplify:

 p− (p + 1)3

Solution

It is known that,

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

\[\   p^3  -  \left( p + 1 \right)^3 \] 

\[ = \left\{ p - \left( p + 1 \right) \right\}\left\{ \left( p \right)^2 + \left( p + 1 \right)^2 + \left( p \right) \times \left( p + 1 \right) \right\}\] 

\[ = \left( - 1 \right)\left( p^2 + p^2 + 1 + 2p + p^2 + p \right)\] 

\[ = \left( - 1 \right)\left( 3 p^2 + 3p + 1 \right)\] 

\[ =  - 3 p^2  - 3p - 1\]

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APPEARS IN

 Balbharati Solution for Balbharati Class 8 Mathematics (2019 to Current)
Chapter 6: Factorisation of Algebraic expressions
Practice Set 6.3 | Q: 2.4 | Page no. 32
Solution Simplify: P3 − (P + 1)3 Concept: Factors of A3 - B3.
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