Question

Factorise 9 (b+2a)square-4asquare​

Answer 1

Factorise:

9( b + 2a )² - (4)²

Solution:

= 3² ( b + 2a )² - (4)²

[ by using : a² × b² = (ab)² ]

= {3(b + 2a}² - ( 4 )²

= ( 3b + 6a )² - ( 4 )²

[ by using : ( a )² - ( b )² = ( a + b )( a - b ) ]

= { (3b + 6a) + 4 } { (3b + 6a) - 4 }

= ( 3b + 6a + 4) ( 3b + 6a - 4 )

( 3b + 6a + 4 ) ( 3b + 6a - 4) is the factorised form.

More:

Factorisation mean expressing an expression as a product of its factors. What is the practical use of the factorisation we did just now? One possible practical use is: let the given expression be the area of a rectangle, then we could factorise it to find the sides of the rectangle.

Answer 2

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Factorise:

Factorise:9( b + 2a )² - (4)²

Factorise:9( b + 2a )² - (4)²Solution:

Factorise:9( b + 2a )² - (4)²Solution:= 3² ( b + 2a )² - (4)²

Factorise:9( b + 2a )² - (4)²Solution:= 3² ( b + 2a )² - (4)²[ by using : a² × b² = (ab)² ]

Factorise:9( b + 2a )² - (4)²Solution:= 3² ( b + 2a )² - (4)²[ by using : a² × b² = (ab)² ]= {3(b + 2a}² - ( 4 )²

Factorise:9( b + 2a )² - (4)²Solution:= 3² ( b + 2a )² - (4)²[ by using : a² × b² = (ab)² ]= {3(b + 2a}² - ( 4 )²= ( 3b + 6a )² - ( 4 )²

Factorise:9( b + 2a )² - (4)²Solution:= 3² ( b + 2a )² - (4)²[ by using : a² × b² = (ab)² ]= {3(b + 2a}² - ( 4 )²= ( 3b + 6a )² - ( 4 )²[ by using : ( a )² - ( b )² = ( a + b )( a - b ) ]

Factorise:9( b + 2a )² - (4)²Solution:= 3² ( b + 2a )² - (4)²[ by using : a² × b² = (ab)² ]= {3(b + 2a}² - ( 4 )²= ( 3b + 6a )² - ( 4 )²[ by using : ( a )² - ( b )² = ( a + b )( a - b ) ]= { (3b + 6a) + 4 } { (3b + 6a) - 4 }

Factorise:9( b + 2a )² - (4)²Solution:= 3² ( b + 2a )² - (4)²[ by using : a² × b² = (ab)² ]= {3(b + 2a}² - ( 4 )²= ( 3b + 6a )² - ( 4 )²[ by using : ( a )² - ( b )² = ( a + b )( a - b ) ]= { (3b + 6a) + 4 } { (3b + 6a) - 4 }= ( 3b + 6a + 4) ( 3b + 6a - 4 )

( 3b + 6a + 4 ) ( 3b + 6a - 4)