Question

Factorise using suitable identity : 4x2 + y2 + 25z2 + 4xy - 10yz -20zx  and hence evaluate for x = 3 , y = 2 and z = -2​

Answer 1

In the given question , we have to factorise -

4x² + y² + 25z² + 4xy - 10yz - 20xz

and evaluate for x = 3 , y = 2 and z = -2 .

Solution -

To Factorise -

4x² + y² + 25z² + 4xy - 10yz - 20xz

=> { 2x }² + { y }² + { - 5z }² + 2 { 2x }[ y } + 2 { y }{ -5 z } + 2 { 2x }[ -5 z }

=> [ 2x + y - 5z ] ² or [ 5z - 2x - y ]²

This is the required answer .

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Additional Information -

[ a + b + c ] ² = a² + b² + c² + 2ab + 2bc + 2ac

[ a + b - c ]² = a² + b² + c² + 2ab - 2bc - 2ac

[ a - b + c ]² = a² + b² + c²- 2ab - 2bc + 2ac

[ -a + b + c ]² = a² + b² + c² - 2ab + 2bc - 2ac

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