Question

p^2q^2-6pqr+9r^2( Factorise)

Answer 1

We need to know algebraic identity first.

   (a - b)² = a² - 2ab + b²

Solution :

    Now, p²q² - 6pqr + 9r²

          = (pq)² - (2 * pq * 3r) + (3r)²

          = (pq - 3r)²

          = (pq - 3r) (pq - 3r),

which is the required factorization.

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Answer 2

Answer :-

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To factorise of : p²q² - 6pqr + 9r²


Salutation :-


p²q² - 6pqr + 9r²

= ( pq )² - 2 × pq × 3r + ( 3r )²

= ( pq - 3r )²

= ( pq - 3r ) ( pq - 3r ) [ ★ Required answer ]

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Verification :-

( pq - 3r ) ( pq - 3r )

= pq ( pq - 3r ) - 3r ( pq - 3r )

= p²q² - 3pqr - 3pqr + 9r²

= p²q² - 6pqr + 9r² [ ★ Proved ]

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Used identity :-

( a - b )² = a² - 2ab + b²

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