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Question
Simplify
(4x²-9y²)³+(9y²-16z²)³+(16z²-4x²)³
(4x²-9y²)³+(9y²-16z²)³+(16z²-4x²)³
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Solution
the problem is in the form (a-b)3 + (b-c)3 + (c-a)3
on simplyfiying them
Let x = (a – b), y = (b – c) and z = (c – a)
Consider, x + y + z = (a – b) + (b – c) + (c – a) = 0
⇒ x3 + y3 + z3 = 3xyz
That is (a – b)3 + (b – c)3 + (c – a)3 = 3(a – b)(b – c)(c – a)
here a=4x^2 ; b=9y^2 ; c=16z^2
(4x²-9y²)³+(9y²-16z²)³+(16z²-4x²)³ = 3(4x²-9y²)(9y²-16z²)(16z²-4x²)
hope it helps
on simplyfiying them
Let x = (a – b), y = (b – c) and z = (c – a)
Consider, x + y + z = (a – b) + (b – c) + (c – a) = 0
⇒ x3 + y3 + z3 = 3xyz
That is (a – b)3 + (b – c)3 + (c – a)3 = 3(a – b)(b – c)(c – a)
here a=4x^2 ; b=9y^2 ; c=16z^2
(4x²-9y²)³+(9y²-16z²)³+(16z²-4x²)³ = 3(4x²-9y²)(9y²-16z²)(16z²-4x²)
hope it helps
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