Question

factorise 9 X square + 16 y square + 25 z square + 24 x y - 40 y z -30 ZX

Answer 1

9x²+16y²+25z²+24xy-40yz-30zx
(3x)²+(4y)²+(-5z)²+(2*3x*4y)+(2*4y*-5z)+(2*-5z*3x)
(3x+4y-5z)²

Answer 2

Given : 9x² + 16y² + 25z² + 24xy - 40yz - 30zx

To Find : Factorize

Solution:

9x² + 16y² + 25z² + 24xy - 40yz - 30zx

= (3x)² + (4y)² + (5z)² + 2(3x)(4y)  - 2(4y)(5z)  - 2(3x)(5z)

= (3x)² + (4y)² + (-5z)² + 2(3x)(4y)  + 2(4y)(-5z)  + 2(3x)(-5z)

= (3x)² + (4y)² + (-5z)² + 2(3x)(4y)  + 2(4y)(-5z)  + 2(3x)(-5z)

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

a = 3x

b = 4y

c = - 5z

= ( 3x + 4y - 5z)²

9x² + 16y² + 25z² + 24xy - 40yz - 30zx =  ( 3x + 4y - 5z)²

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