Factorise the following 4(a+b)^2-9(a-b)^2
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Answer:
4(a+
b)
2
−
9(a−
b)
2
By using identity
a 2
b 2
(a+
b)(a−
b)
It can be factorised as
4(a+
b)
2
−
9(a−
b)
2
=
[(2(a+
b))
2
−
(3(a−
b))
2
]
= [2(a+ b)+ 3(a− b)][2(a+ b)− 3(a− b)]
= [2a+ 2b+ 3a− 3b][2a+ 2b− 3a+ 3b]
= (5a− b)(5b− a)
Thus factors are
5a−
b,5b−
a
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