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प्रश्न
Simplify:
p3 − (p + 1)3
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:
\[\frac{8 x^3 - 27 y^3}{4 x^2 - 9 y^2}\]
Simplify:
\[\frac{x^2 - 5x - 24}{\left( x + 3 \right)\left( x + 8 \right)} \times \frac{x^2 - 64}{\left( x - 8 \right)^2}\]
Simplify:
\[\frac{3 x^2 - x - 2}{x^2 - 7x + 12} \div \frac{3 x^2 - 7x - 6}{x^2 - 4}\]
Simplify:
\[\frac{4 x^2 - 11x + 6}{16 x^2 - 9}\]
Simplify:
\[\frac{a^3 - 27}{5 a^2 - 16a + 3} \div \frac{a^2 + 3a + 9}{25 a^2 - 1}\]
Factorise:
y3 − 27
Factorise:
x3 − 64y3
Factorise:
64x3 − 729y3
Simplify: (2x + 3y)3 - (2x - 3y)3
Factorise the following:
27x3 – 8y3
