Question

सोपे रूप द्या: p³ - (p + 1)³

Answer 1

सोपे रूप द्या: p³ - (p + 1)³

${a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} ) \\ \\ a = p \\ \\ b = p + 1 \\ \\ {p}^{3} - ( {p + 1)}^{3} = (p - (p + 1))( {p}^{2} + (p)(p + 1)+ {(p + 1)}^{2} ) \\ \\ = (p - p -1 )( {p}^{2} + {p}^{2} + p + {p}^{2} + 2p + 1) \\ \\ = ( - 1)(3 {p}^{2} + 3p + 1)$

${p}^{3} - ( {p + 1)}^{3} = ( - 1)(3 {p}^{2} + 3p + 1)$

Answer 2

Answer:

p³ - (p + 1)³

\begin{gathered} {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} ) \\ \\ a = p \\ \\ b = p + 1 \\ \\ {p}^{3} - ( {p + 1)}^{3} = (p - (p + 1))( {p}^{2} + (p)(p + 1)+ {(p + 1)}^{2} ) \\ \\ = (p - p -1 )( {p}^{2} + {p}^{2} + p + {p}^{2} + 2p + 1) \\ \\ = ( - 1)(3 {p}^{2} + 3p + 1) \\ \\ \end{gathered}

a

3

−b

3

=(a−b)(a

2

+ab+b

2

)

a=p

b=p+1

p

3

−(p+1)

3

=(p−(p+1))(p

2

+(p)(p+1)+(p+1)

2

)

=(p−p−1)(p

2

+p

2

+p+p

2

+2p+1)

=(−1)(3p

2

+3p+1)

\begin{gathered} {p}^{3} - ( {p + 1)}^{3} = ( - 1)(3 {p}^{2} + 3p + 1) \\ \\ \end{gathered}

p

3

−(p+1)

3

=(−1)(3p

2

+3p+1)