Question

Factorise = 4x^2+12xy+9y^2-50x-75y

Answer 1

QUESTION:-
4x²+12xy+9y²-50x-75y
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→4x²+12xy+9y² becomes formula of (2x+3y)²

→(2x+3y)²-25(2x+3y)
Taking (2x+3y) as common

→(2x+3y){(2x+3y)-25(1)}

→(2x+3y)(2x+3y-25) ANSWER

Answer 2

Hello Mate!

=> 4x² + 12xy + 9y² - 50x - 75y

Here, we notice that 4x² can be written as (2x)² and 9y² as (3y)².

=> (2x)² + 2 × 2 × 3xy + (3y)² - 50x - 75y

So, (2x)² + 2 × 2 × 3xy + (3y)² seems similar to a² + 2ab + b² which is equal to ( a + b )².

=> ( 2x + 3y )² - 50x - 75y

Taking - 25 common from - 50x and - 75y we get,

=> ( 2x + 3y )² - 25( 2x + 3y )

Again taking ( 2x + 3y ) common we get,

=> ( 2x + 3y )[ ( 2x + 3y ) - 25 ]

=> ( 2x + 3y )( 2x + 3y - 25 )

Hence concepts used - Formula and taking common factors out.

Have great future ahead!