Question

Simplify:   (4x²-9y²)³+ (9y²-16z²)³+(16z²-4x²)³/(2x -3y)³+(3y - 4z )³+(4z - 2x )³
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Answer 1

we have to simplify this : (4x²-9y²)³+ (9y²-16z²)³+(16z²-4x²)³/(2x -3y)³+(3y - 4z )³+(4z - 2x )³

solution : you have to understand one of the most important algebraic applications.

if a + b + c = 0 ⇒ a³ + b³ + c³ = 3abc

here (4x² - 9y²)³ + (9y² - 16z²)³ + (16z² - 4x²)³

let a = 4x² - 9y² , b = 9y² - 16z² , c = 16z² - 4x²

now, a + b + c = (4x² - 9y²) + (9y² - 16z²) + (16z² - 4x²) = 0

so a³ + b³ + c³ = (4x² - 9y²)³+ (9y²- 16z²)³+(16z² - 4x²) = 3(4x² - 9y²)(9y² - 16z²)(16z² - 4x²) ....(1)

similarly,

let a = (2x - 3y) , b = (3y - 4z) and c = (4z - 2x)

a + b + c = (2x - 3y) + (3y - 4z) + (4z - 2x) = 0

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

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

from equations (1) and (2),

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

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

Therefore the answer is (2x + 3y)(3y + 4z)(4z + 2x)

Answer 2

Step-by-step explanation:

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