(i) a(a – 2) – b(b – 2)
(ii) a(a – 1) – b(b – 1)
Answer :
(i) a(a – 2) – b(b – 2)
Above question can be written as,
a2 – 2a – b2 – 2b
Rearranging the above terms, we get,
a2 – b2 – 2a – 2b
We know that, a2 – b2 = (a + b) (a – b)
[(a + b)(a – b)] – 2(a – b)
Take out common in all terms,
(a – b) (a + b – 2)
(ii) a(a – 1) – b(b – 1)
a(a – 1) – b(b – 1)
Above question can be written as,
a2 – a – b2 + b
Rearranging the above terms, we get,
a2 – b2 – a + b
We know that, a2 – b2 = (a + b) (a – b)
[(a + b) (a – b)] – 1 (a – b)
Take out common in all terms,
(a – b) (a + b – 1)
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