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प्रश्न
Factorise:
a6 – 15625b6
बेरीज
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उत्तर
Given expression is a6 – 15625b6
Applying the identity, we get,
⇒ (a3)2 – [(5b)3]2 = (a3 + [5b)3] [a3 – (5b)3]
We have
⇒ [a3 + (5b)3] = (a + 5b) [a2 – 5ab + (5b)2]
And
⇒ [a3 – (5b)3] = (a – 5b) [a2 + 5ab + (5b)2]
By grouping all these terms, we get,
⇒ (a + 5b) (a – 5b) (a2 – 5ab + 25b2) (a2 + 5ab + 25b2)
⇒ (a + 5b) (a – 5b) (a4 + 5a3b + 25a2b2 – 5a3b – 25a2b2 – 125ab3 + 25a2b2 + 125ab3 + 625b4
⇒ (a + 5b) (a – 5b) (a4 + 625b4 + 25a2b2)
Hence, factors for the expression a6 – 15625b6 is (a + 5b) (a – 5b) (a4 + 625b4 + 25a2b2)
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