Question

Find the binomial which is a common factor of 9a ^ 2 - 64b ^ 2 and 9a ^ 2 - 24ab + 16b​

Answer 1

Answer:

Step-by-step explanation:

To factorise of : 9a² - 24ab + 16b²

Salutation :-

9a² - 24ab + 16b²

= ( 3a )² - 2 × 3a × 4b + ( 4b )²

= ( 3a - 4b )² [ • Using identity ]

= ( 3a - 4b ) ( 3a - 4b ) [ • Required answer ]

___________________________

Verification :-

( 3a - 4b ) ( 3a - 4b )

= 3a ( 3a - 4b ) - 4b ( 3a - 4b )

= 9a² - 12ab - 12ab + 16b²

= 9a² - 24ab + 16b² [ • Proved ]

_____________________________

Used identity :-

( a - b )² = a² - 2ab + b²