Question

factorise... 8a³-b³-4ax+2bx​

Answer 1

Answer:

( 2a - b ) ( 4a² + b² + 2ab - 2x )

Step-by-step explanation:

Given---> 8a³ - b³ - 4ax + 2bx

To find---> Factors of given expression

Solution---> We know that

x³ - y³ = ( x - y ) ( x² + y² + xy )

Now returning to original problem we get,

8a³ - b³ - 4ax + 2bx

= ( 2a )³ - ( b )³ - 4ax + 2bx

Applying above identity , we get,

= ( 2a - b ) { ( 2a )² + ( b )² + 2a b } - 2x ( 2a - b )

= ( 2a - b ) ( 4a² + b² + 2ab ) - 2x ( 2a - b )

Taking ( 2a - b ) common from both terms

= ( 2a - b ) ( 4a² + b² + 2ab - 2x )

Additional information--->

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) a² - b² = ( a + b ) ( a - b )

5) ( a + b )² = a² + b² + 2ab

6) ( a - b )² = a² + b² - 2ab

Answer 2

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          Step-by-step explanation:

8a³– b³– 4ax + 2bx

= (2a)³ – (b)³ – 2x(2a – b)

We know, a³ – b³ = (a – b)(a² + ab + b²)

= (2a – b) ((2a)² + 2a.b + (b)²) – 2x(2a – b)

= (2a – b) (4a² + 2ab + b²) – 2x(2a – b)

= (2a – b) (4a² + 2ab + b² – 2x)