Question

(ax+by)²-(bx+ay)² .simplify

Answer 1

Answer:

( x + y ) ( x - y ) ( a + b ) ( a - b )

Step-by-step explanation:

Given---> ( ax + by )² - ( bx + ay )²

To find---> Factors of given expression

Solution---> We know that,

a² - b² = ( a + b ) ( a - b )

Now , returning to original problem,

( ax + by )² - ( bx + ay )²

= { ( ax + by ) + ( bx + ay ) } { ( ax + by ) - ( bx + ay ) }

= ( ax + by + bx + ay ) ( ax + by - bx - ay )

= ( ax + ay + bx + by ) ( ax - ay - bx + by )

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

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

= ( x + y ) ( x - y ) ( a + b ) ( a - b )

Additional identies --->

1) ( a + b )² = a² + b² + 2ab

2) ( a - b )² = a² + b² - 2ab

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

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