Question

Express as the square of a trinomial:

$3a2 + 2b2 + c2 - 2 \sqrt{} 6 ab + 2 \sqrt{} 3 ac - 2 \sqrt{} 2bc$



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Answer 1

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Answer 2

Answer:

Required factorised form of the given equation is ( - √3 a + √2 b - c )^2.

Step-by-step-explanation:

Your question needs a correction.

$\text{Correct Question} : 3a^2 + 2b^3 + c^2 - 2 \sqrt{6} ab + 2 \sqrt{3} ac - 2 \sqrt{2} bc$

Since we have to express this equation as the square of a trinomial, we have to apply ( a + b + c )^2 = a^2 + b^2 + c^2 + 2( ab + bc + ac ), where a or b or c can be negative too.

Note: a, b and c, in the above statement, are different from the coefficients given in this question.

= > 3a^2 + 2b^2 + c^2 - 2√6 ab + 2√3 ac - 2√2 bc

= > ( - √3 a )^2 + ( √2 b )^2 + ( - c )^2 + 2( - √6 ab + √3 ac - √2 bc )

= > ( - √3 a )^2 + ( √2 b )^2 + ( - c )^2 + 2[ ( - √3 a )( √2 b ) + ( - √3 a )( - c ) + ( √2 b )( - c ) ]

= > [ ( - √3 a ) + ( √2 b ) + ( - c ) ]^2 { by using the formula given above }

= > [ - √3 a + √2 b - c ]^2

Hence the required factorised form of the given equation is ( - √3 a + √2 b - c )^2.