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प्रश्न
Simplify:
(a + b)3 − a3 − b3
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उत्तर
It is known that,
a3 − b3 = (a − b)(a2 + ab + b2)
(a + b)3 − a3 − b3
= (a + b)3 − (a3 + b3)
= (a + b)3 −{(a + b)(a2 + b2 − ab)}
= (a + b) {(a + b)2 − (a2 + b2 − ab)}
= (a + b) (a2 + b2 + 2ab − a2 − b2 + ab)
= (a + b) (3ab)
= 3a2b + 3ab2
संबंधित प्रश्न
Simplify:
\[\frac{a^2 + 10a + 21}{a^2 + 6a - 7} \times \frac{a^2 - 1}{a + 3}\]
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:
\[\frac{4 x^2 - 11x + 6}{16 x^2 - 9}\]
Factorise:
125y3 − 1
Factorise:
8p3 −\[\frac{27}{p^3}\]
Factorise:
`16a^3 - 128/b^3`
Simplify:
(3xy − 2ab)3 − (3xy + 2ab)3
Factorise: 54p3 - 250q3.
Factorise: `a^3 - 1/(a^3)`
