Question

if x/2y =2y/3z, then show that x^2+4y^2+9z^2=(x-2y+3z)(x+2y+3z)

Answer 1

x/2y=2y/3z
x*3z=4y²
x²+4y²+9z²=x²+3xz+9z²
=x²+2*x*3z+9z²-3xz
=(x+3z)²-4y²
=(x+3z+2y)(x+3z-2y)
=(x-2y+3z)(x+2y+3z)

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