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प्रश्न
Simplify:
p3 − (p + 1)3
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उत्तर १
It is known that,
a3 − b3 = (a − b)(a2 + ab + b2)
p3 − (p + 1)3
= {p − (p + 1)} {(p)2 + (p + 1)2 + (p) × (p + 1)}
= (−1) (p2 + p2 + 1 + 2p + p2 + p)
= (−1)(3p2 + 3p + 1)
= −3p2 − 3p − 1
उत्तर २
p3 − (p + 1)3
We know that,
(a + b)3 = a3 + 3a2b + 3ab2 + b3
= p3 − (p3 + 3p2 + 3p + 1)
= p3 − p3 − 3p2 − 3p − 1
= −3p2 − 3p − 1
संबंधित प्रश्न
Simplify:
\[\frac{m^2 - n^2}{\left( m + n \right)^2} \times \frac{m^2 + mn + n^2}{m^3 - n^3}\]
Simplify:
\[\frac{a^2 + 10a + 21}{a^2 + 6a - 7} \times \frac{a^2 - 1}{a + 3}\]
Simplify:
\[\frac{3 x^2 - x - 2}{x^2 - 7x + 12} \div \frac{3 x^2 - 7x - 6}{x^2 - 4}\]
Factorise:
y3 − 27
Factorise:
8p3 −\[\frac{27}{p^3}\]
Simplify:
(a + b)3 − a3 − b3
Factorise: x3 - 8y3
Factorise: `a^3 - 1/(a^3)`
Simplify: (a - b)3 - (a3 - b3)
Factorise the following:
a6 – 64
