Question

1) 24x2 -41x+12 factorise
2) factorise (p-q)3 +(q-r)3+(r-p)3.
pllź hlp

Answer 1

1) 24x² - 41x + 12

= 24x² - 32x - 9x +12

= 8x ( 3x - 4 ) - 3 ( 3x - 4 )

= ( 3x - 4 ) ( 8x - 3 ).

2). ( p - q )³ + ( q - r )³ + ( r - p )³

Let ( p - q ) = A  ----- ( 1 )

      ( q - r ) = B  ------ ( 2 )

      ( r - p ) = C ------ ( 3 )


By adding ( 1 ),( 2 ) and ( 3 ).

 ⇒ p - q + q - r + r - p = A + B + C

 ⇒ 0 = A + B + C

We know that if ( A + B + C = 0 ) , then A³ + B³ + C³ = 3ABC.

By substituting the values of A , B and C.

⇒ ( p - q )³ + ( q - r )³ + ( r - p )³ = 3 ( p - q ) ( q - r ) ( r - p ).

Answer 2

Answer:

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Step-by-step explanation

1) 24x² - 41x + 12

= 24x² - 32x - 9x +12

= 8x ( 3x - 4 ) - 3 ( 3x - 4 )

= ( 3x - 4 ) ( 8x - 3 ).

2). ( p - q )³ + ( q - r )³ + ( r - p )³

Let ( p - q ) = A  ----- ( 1 )

     ( q - r ) = B  ------ ( 2 )

     ( r - p ) = C ------ ( 3 )

By adding ( 1 ),( 2 ) and ( 3 ).

 ⇒ p - q + q - r + r - p = A + B + C

 ⇒ 0 = A + B + C

We know that if ( A + B + C = 0 ) , then A³ + B³ + C³ = 3ABC.

By substituting the values of A , B and C.

⇒ ( p - q )³ + ( q - r )³ + ( r - p )³ = 3 ( p - q ) ( q - r ) ( r - p ).