Mathematics for C
4x² - y² + 6y -9.
Answers
Answer:
( 2x + y - 3 ) ( 2x - y + 3 )
Step-by-step explanation:
To find ---> Factors of 4x² - y² + 6y - 9
Solution--->
4x² - y² + 6y - 9
= ( 2x )² - ( y² - 6y + 9 )
= ( 2x )² - { ( y )² - 2 × ( 3 ) (y ) + ( 3 )² }
We have an idemtity as follows,
( a - b )² = a² + b² - 2ab , applying it here , we get
= ( 2x )² - ( y - 3 )²
We have an identity a² - b² = ( a + b ) ( a - b ) , applying it here we get,
= { 2 x + ( y - 3 ) } { 2x - ( y - 3 ) }
= ( 2x + y - 3 ) ( 2x - y + 3 )
Additional identities--->
(1) (a + b )² = a² + b² +2ab
(2) (x + a ) ( x + b ) = x² + ( a + b ) x +ab
(3) ( a + b )³ = a³ + b³ + 3ab ( a + b )
(4) ( a - b )³ = a³ - b³ - 3ab ( a - b )
Answer:
Step-by-step explanation:
4x² - y² + 6y - 9
= ( 2x )² - ( y² - 6y + 9 )
= ( 2x )² - { ( y )² - 2 × ( 3 ) (y ) + ( 3 )² }
we know that
( a - b )² = a² + b² - 2ab ,
= ( 2x )² - ( y - 3 )²
AS a² - b² = ( a + b ) ( a - b ) ,
= { 2 x + ( y - 3 ) } { 2x - ( y - 3 ) }