Question

9a^2-24ab+16b^2(Factorise)

Answer 1

Answer :-

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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 ]

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Verification :-

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

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

= 9a² - 12ab - 12ab + 16b²

= 9a² - 24ab + 16b² [ • Proved ]

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Used identity :-

( a - b )² = a² - 2ab + b²

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Answer 2

We need to know algebraic identity first.

    (a - b)² = a² - 2ab + b²

Solution :

    Now, 9a² - 24ab + 16b²

          = (3a)² - (2 * 3a * 4b) + (4b)²

          = (3a - 4b)²

          = (3a - 4b) (3a - 4b),

which is the required factorization.

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