Question

plz solve this question ​

Answer 1

Answer:

3(2x+3y)(3y+4z)(4z+2x)

Step-by-step explanation:

Let 4x²-9y² be a

Let 9y²-16z² be b

Let 16z²-4x² be c

We know that when a+b+c=0, then a³+b³+c³=3abc

a+b+c→

(4x²-9y²)+(9y²-16z²)+(16z²-4x²)=4x²-9y²+9y²- 16z²+16z²-4x²=0

Therefore, (4x²-9y²)³+(9y²-16z²)³+(16z²-4x²)³=3(4x²-9y²)(9y²-16z²)(16y²-4z²)

Similarly, (2x-3y)³+(3y-4z)³+(4z-2x)³=3(2x-3y)(3y-4z)(4z-2x)

3(4x²-9y²)(9y²-16z²)(16z²-4x²)=3{(2x)²-(3y)²}{(3y)²-(4z)²}{(4z)²-(2x)²}

using a²-b² = (a+b)(a-b)

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

Therefore, (4x²-9y²)³+(9y²-16z²)³+(16z²-4x²)³ /(2x-3y)³+(3y-4z)³+(4z-2x)³

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

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