Question

x3+64y3-125+60xy factorise ​

Answer 1

Step-by-step explanation:

We know that

x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – zx).

Answer 2

Answer:

( x + 4y - 5 ) ( x² + 16y² + 25 + 5x - 4xy + 20y )

Step-by-step explanation:

Given----> x³ + 64y³ - 125 + 60xy

To find ----> We know that,

x³+ y³ + z³ - 3xyz

= ( x + y + z ) ( x² + y² + z² - xy - yz - zx )

Now,

x³ + 64y³ - 125 + 60xy

= ( x )³ + ( 4y )³ + ( - 5 )³ - 3 ( x ) ( 4y ) ( - 5 )

Applying above identity, we get,

={ x + 4y + ( - 5 ) } { x² + ( 4y )² + ( - 5 )² - ( x ) ( - 5 )

- ( x ) ( 4y ) - ( 4y ) ( - 5 ) }

= (x + 4y - 5 ) ( x² + 16y² + 25 + 5x - 4xy + 20y )

Additional identity------>

1) ( a + b )² = a² + b² + 2ab

2) ( a - b )² = a² + b² - 2ab

3) ( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ca

4) ( a + b )³ = a³ + b³ + 3ab ( a + b )

5) ( a - b )³ = a³ - b³ - 3ab ( a - b )

6) ( a³ + b³ ) = ( a + b ) ( a² + b² - ab )

7) ( a³ - b³ ) = ( a - b ) ( a² + b² + ab )

8) ( a² - b² ) = ( a + b ) ( a - b )