Simplify
(4.5a + 1.5b)2 + (4.5b + 1.5a)2
The given expression is
(4.5a + 1.5b)2 + (4.5b + 1.5a)2
We have,
(4.5a + 1.5b)2 = (4.5a)2 + 2(4.5a)(1.5b) + (1.5b)2
and
(4.5b + 1.5a)2 = (4.5b)2 + 2(4.5b)(1.5a) + (1.5a)2
Therefore,
(4.5a + 1.5b)2 + (4.5b + 1.5a)2
= (4.5a)2 + 2(4.5a)(1.5b) + (1.5b)2 + (4.5b)2 + 2(4.5b)(1.5a) + (1.5a)2
= (4.5)2(a2 + b2) + 2.2(4.5)(1.5)ab + (1.5)2(a2 + b2)
= (a2 + b2)( (4.5)2 + (1.5)2) + 27ab
= 22.5(a2 + b2) + 27ab
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