Question

(3x-5y)^3-(5x-2y)^3+(2x+3y)^3. Please factorise it.

Answer 1

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Here's your answer...

Let (3x-5y) = a
-(5x-2y) = b
(2x+3y) =c

If you look carefully, you'll see that a+b+c = 0

When a+b+c = 0, a³+b³+c³ = 3abc

So the polynomial in the question becomes...
-3(3x-5y)(5x-2y)(2x+3y)

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Answer 2

Answer:

−3(3x−5y)(5x−2y)(2x+3y)

Step-by-step explanation:

let a=3x−5y, $$b = 2y - 5x andc = 2x + 3y$$

∴a+b+c=0

Hence, a

3

+b

3

+c

3

=3abc

So, (3x−5y)

3

−(5x−2y)

3

+(2x+3y)

3

=3(3x−5y)(2y−5x)(2x+3y)

=−3(3x−5y)(5x−2y)(2x+3y)