Question

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Answer 1

Given:

∑ab(a + b) + 2abc = (a + b) (b + c) (a + c)

To find:

show that; ∑ab(a + b) + 2abc = (a + b) (b + c) (a + c)

Solution:

From given, we have,

∑ab(a + b) + 2 abc

[ ∑ ab(a + b) ] + 2 abc

= ab(a + b) + bc(b + c) + ca(c + a) + 2 abc

= a²b + ab² + b²c + bc² + c²a + ca² + 2 abc

= L.H.S

(a + b) (b + c) (a + c)

= (ab + ac + b² + bc) (a + c)

= a²b + abc + a²c + ac² + ab² + bc² + abc + bc²

= a²b + ab² + b²c + bc² + c²a + ca² + 2 abc

= R.H.S

As L.H.S = R.H.S

Hence proved.