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प्रश्न
Factorise the following:
a6 – 64
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उत्तर
a6 – 64 = a6 – 26
= (a2)3 – (22)3 ...[a3 – b3 = (a – b) + (a2 + ab + b2)]
= (a2 – 22) [(a2)2 + (a2) (22) + (22)2]
= (a + 2) (a – 2) (a4 + 4a2 + 16)
= (a + 2) (a – 2) [(a2)2 + 42 + 8a2 – 4a2]
= (a + 2) (a – 2) [(a2 + 4)2 – (2a)2] ......{a2 – b2 = (a + b) (a – b)}
= (a + 2) (a – 2) (a2 + 4 + 2a) (a2 + 4 – 2a)
= (a + 2) (a – 2) (a2 + 2a + 4) (a2 – 2a + 4)
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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:
\[\frac{a^2 + 10a + 21}{a^2 + 6a - 7} \times \frac{a^2 - 1}{a + 3}\]
Factorise:
y3 − 27
Factorise:
125y3 − 1
Factorise:
8p3 −\[\frac{27}{p^3}\]
Factorise:
`16a^3 - 128/b^3`
Simplify:
(3xy − 2ab)3 − (3xy + 2ab)3
Factorise: x3 - 8y3
Simplify: (2x + 3y)3 - (2x - 3y)3
Factorise the following:
27x3 – 8y3
