Mathematics
Factorise :
25(2a - b)2 - 81b2
Factorisation
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Answer
Given,
25(2a - b)2 - 81b2
= [5(2a - b)]2 - (9b)2
= [5(2a - b) + 9b][5(2a - b) - 9b]
= (10a - 5b + 9b)(10a - 5b - 9b)
= (10a + 4b)(10a - 14b)
= 2(5a + 2b) × 2(5a - 7b)
= 4(5a + 2b)(5a - 7b).
Hence, 25(2a - b)2 - 81b2 = 4(5a + 2b)(5a - 7b).
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