Factories the following
4 (a + b)2 – 9 (a – b)2
In the given expression
We know that
(a + b)2 = a2 + 2ab + b2
(a-b)2 = a2-2ab + b2
Hence
4[a2 + 2ab + b2] – 9[a2-2ab + b2]
4a2 + 8ab + 4b2 - 9a2 + 18ab - 9b2
26ab – 5a2 - 5b2
25ab + ab – 5a2 – 5b2
[25ab – 5a2] + [ab – 5b2]
5a[5b – a] – b[5b – a]
[5a – b][5b – a]
Hence the factors 4 (a + b)2 – 9 (a – b)2 are [5a – b] and [5b – a]
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