Q. 84 K5.0( 3 Votes )

Simplify<

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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