Question

Factorize
$9x {}^{2} + y { }^{2} + z {}^{2} - 6xy + 2yz - 6xz$
Then find the value when x=1, y=2 and z = - 1

Answer 1

x = 1

Y = 2

z = - 1

9x^2 + y^2 + z^2 - 6xy + 2yz - 6xz

=> (-3x)^2 + (y)^2 + (z)^2 + 2(-3x)(y) + 2(y)(z) + 2(z)(-3x)

=> ( - 3x + y + z) ^2


Now,

On putting the values of x, y, and z, we get

= [ (- 3 × 1) + 2 + (-1)]^2

= ( - 3 + 2 - 1)^2

= (-2)^2

= 4

Answer 2

Hey friend ☺

☆ FACTORIZATION ☆

9x^2 + y^2 + z^2 - 6xy + 2yz - 6xz

= ( -3 )^2 + ( y )^2 + ( z )^2 + 2 ( -3x )( y ) + 2 ( y ) ( z ) + 2 ( -3x ) ( z )

= ( - 3x + y + z )^2

If x = 1 , y = 2 & z = -1

then

( - 3x + y + z )^2

= ( -3 ( 1 ) + 2 - 1 )^2

= ( - 3 + 2 - 1 )^2

= ( - 2 )^2

= 4

Hope it helps you

✌