without actually calculating cubes find the value of 125(x-y)∧3+(5y-3z)∧3+(3z-5x)∧3
Answers
Answer:
Value of Given Expression is -135xz² - 225y²z + 135yz² - 375x²y + 225x²y + 375xy²
Step-by-step explanation:
To find value of: 125 ( x - y )³ + ( 5y - 3z )³ + ( 3x - 5x )³
We use a result which states,
if a + b + c = 0
then a³ + b³ + c³ = 3abc
Consider, 125 ( x - y )³ + ( 5y - 3z )³ + ( 3x - 5x )³ = ( 5(x - y) )³ + ( 5y - 3z )³ + ( 3x - 5x )³
let, a = 5( x - y ) , b = 5y - 3z and c = 3z - 5x
here, a + b + c = 5( x - y ) + 5y - 3z + 3z - 5x = 5x - 5y + 5y - 3z + 3z - 5x = 0
So, a³ + b³ + c³ = ( 5(x - y) )³ + ( 5y - 3z )³ + ( 3x - 5x )³
= 3( 5(x-y) )( 5y - 3z )( 3z - 5x )
= 15( x - y )( 5y - 3z )( 3z - 5x )
= 15( -9xz² - 15y²z + 9yz² - 25x²y + 15x²y + 25xy² )
= -135xz² - 225y²z + 135yz² - 375x²y + 225x²y + 375xy²
Therefore, Value of Given Expression is -135xz² - 225y²z + 135yz² - 375x²y + 225x²y + 375xy²