Question

factorise 8y3-125x3​

Answer 1

Step-by-step explanation:

To find ---> 8y³ - 125x³

Solution--->

8y³ - 125x³ = ( 2 × 2 × 2× y³ ) - ( 5 × 5 × 5 × x³ )

= ( 2 y )³ - ( 5x )³

We have a formula

a³ - b³ = ( a - b ) (a² + b² + ab ) , applying it , we get

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

= ( 2y - 5x ) ( 4y² + 25x² + 10x )

Additional identities --->

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

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

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

4) ( a + b )² = a² + b² + 2ab

5) ( a - b )² = a² + b² - 2ab

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

7) a² - b² = ( a + b ) ( a - b )

8) ( x + a ) ( x + b ) = x² + ( a + b ) x + ab