Question

4x^2+y^2+z^2-4zy-2yz+4xz factorise

Answer 1

$\bold{\huge{\boxed{Solution:}}}$


4x² + y² + z² - 4zy - 2yz + 4xz

=> (2x)² + y² + z² - 4zy - 2yz + 4xz

=> (2x)² + (-y)² + z² - 4zy - 2yz + 4xz

=> (2x)² + (-y)² + z² + 2(2x)(-y) + 2(-y)(z) + 2(z)(2x)

Using identity:

(a + b+ c)² = a² + b² + c² + 2ab + 2bc + 2ca

Where, a = 2x , b = (-y) , c = z

{ 2x + (-y) + z }²

( 2x - y + z )²

(2x - y + z )( 2x - y + z ) .....answer.
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Answer 2

$\textbf{Solution:}$
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4x² + y² + z² - 4zy - 2yz + 4xz

=> (2x)² + y² + z² - 4zy - 2yz + 4xz

=> (2x)² + (-y)² + z² - 4zy - 2yz + 4xz

=> (2x)² + (-y)² + z² + 2(2x)(-y) + 2(-y)(z) + 2(z)(2x)

Using identity:

(a + b+ c)² = a² + b² + c² + 2ab + 2bc + 2ca

Where, a = 2x , b = (-y) , c = z

{ 2x + (-y) + z }²

( 2x - y + z )²

(2x - y + z )( 2x - y + z ) .....answer.
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