factorise
( 3x-2y) ^ 3 + (2y-4z)^3 + ( 4z-3x)^3
Answers
Answered by
13
6(3x-2y)(y-2z)(4z-3x)
It is absolutely right
It is absolutely right
DhruvkundraiMessi:
please give proper explaination
solve explain it
Answered by
26
Given Equation is (3x - 2y)^3 + (2y - 4z)^3 + (4z - 3x)^3
We know that (a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3
= > 27x^3 - 54x^2y + 36xy^2 - 8y^3 + 8y^3 - 48y^2z + 96yz^2 - 64z^3 + 64z^3 - 144xz^2 + 108x^2z - 27x^3
= > -54x^2y + 108x^2z + 36xy^2 - 144xz^2 - 48y^2z + 96yz^2.
= > -6(9x^2y - 18x^2z - 6xy^2 + 24xz^2 + 8y^2z - 16yz^2)
= > -6(9x^2y - 18x^2z - 12xyz + 12xyz + 24xz^2 - 6xy^2 + 8y^2z - 16yz^2)
= > -6(9x^2y - 18x^2z - 12xyz + 24xz^2 - 6xy^2 + 12xyz + 8y^2z - 16yz^2)
= > -6(3x(3xy - 6xz - 4yz + 8z^2) - 2y(3xy - 6xz - 4yz + 8z^2))
= > -6(3x - 2y)(3xy - 6xz - 4yz + 8z^2)
= > -6(3x - 2y)(3x(y - 2z) - 4z(y - 2z))
= > -6(3x - 2y)(3x - 4z)(y - 2z).
Hope this helps!
Ok guruji!.. Next time... i wont repeat it.
i m not able to understand the 4th step
I have taken 6 common from it!
Remove all opposite y terms and x terms
No, that I have understood but how 12 came in the brackets
if a + b + c = 0 then a³ + b³ + c³ = 3abc Use this
Ohhhhhh
This will makes it so easier
ok guruji. I will make use of that formula from next time!
Thanks alot
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