Question

simplify(4x^2-9y^2)^3+(9y^2-16y^2)^3+(16z^2-4x^2)^3/(2x-3y)^3+(3y-4z)^3+(4z-2x)^3
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Answer 1

Answer:

The correct term is:

(4x^2-9y^2)^3+(9y^2-16z^2)^3+(16z^2-4x^2)^3 / (2x-3y)^2+(3y-4z)^2+(4z-2x)^3

To find: Simplify the above term.

Solution:

Now the given term is :

(4x^2-9y^2)^3+(9y^2-16z^2)^3+(16z^2-4x^2)^3 ÷

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

Now we know that :

If a + b + c = 0 then a^3 + b^3 + c^3 = 3abc

So applying it, we get:

If ( (2x)^2 - (3y)^2 ) + ( (3y)^2 - (4z)^2 ) + ( (4z)^2 - (2x)^2 ) = 0

Then :

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

= 3( (2x)^2 - (3y)^2 )×( (3y)^2 - (4z)^2 )×( (4z)^2 - (2x)^2 )

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

Now similarly we have:

If ( 2x - 3y ) + ( 3y - 4z ) + ( 4z - 2x ) = 0

Then :

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

Now putting (i) and (ii) together, we get:

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

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

Cancelling common terms, we get:

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

Answer:

So the simplified answer of the term given is 3(2x + 3y)(3y + 4z)(4z + 2x)

Answer 2

Answer:

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