(a^2-4)(9-b^2) +24ab
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(a^2 - 4)(9 - b^2) + 24ab
= 9a^2 - 36 - a^2 b^2 + 4b^2 + 24ab
= 9a^2 + 4b^2 + 24ab - a^2 b^2 - 36
= 9a^2 + 4b^2 + 12ab + 12ab - a^2 b^2 - 36
= [ (3a)^2 + (2b)^2 + 2(3a)(2b)] - 1[ a^2 b^2 - 12ab + 36]
= ( 3a + 2b)^2 - [ (ab)^2 - 2(ab)(6) + (6)^2]
= (3a+2b)^2 - (ab-6)^2
= (3a + 2b - ab + 6) (3a + 2b + ab -6)
= 9a^2 - 36 - a^2 b^2 + 4b^2 + 24ab
= 9a^2 + 4b^2 + 24ab - a^2 b^2 - 36
= 9a^2 + 4b^2 + 12ab + 12ab - a^2 b^2 - 36
= [ (3a)^2 + (2b)^2 + 2(3a)(2b)] - 1[ a^2 b^2 - 12ab + 36]
= ( 3a + 2b)^2 - [ (ab)^2 - 2(ab)(6) + (6)^2]
= (3a+2b)^2 - (ab-6)^2
= (3a + 2b - ab + 6) (3a + 2b + ab -6)
HimanshuRG:
thank you
Answered by
1
(a^2 - 4)(9 - b^2) + 24ab
= 9a^2 - 36 - a^2 b^2 + 4b^2 + 24ab
= 9a^2 + 4b^2 + 24ab - a^2 b^2 - 36
= 9a^2 + 4b^2 + 12ab + 12ab - a^2 b^2 - 36
= [ (3a)^2 + (2b)^2 + 2(3a)(2b)] - 1[ a^2 b^2 - 12ab + 36]
= ( 3a + 2b)^2 - [ (ab)^2 - 2(ab)(6) + (6)^2]
= (3a+2b)^2 - (ab-6)^2
= (3a + 2b - ab + 6) (3a + 2b + ab -6)
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