Question

7(x-2y)² -25(x-2y)+12

Answer 1

ANSWER:

• Required Factorisation = (x-2y-3)(7x-14y-4)

GIVEN:

• 7(x-2y)² -25(x-2y)+12

TO FIND:

• Factorise the above expression.

SOLUTION:

= 7(x-2y)² -25(x-2y)+12

Let (x-2y) = a.

= 7a²-25a+12

= 7a²-21a-4a+12

= (7a²-21a)+(-4a+12)

= 7a(a-3)-4(a-3)

= (a-3)(7a-4)

Putting a = (x-2y)

= (x-2y-3)(7x-14y-4)

Required Factorisation = (x-2y-3)(7x-14y-4)

NOTE:

Some important formulas:

(a+b)² = a²+b²+2ab

(a-b)² = a²+b²-2ab

(a+b)(a-b) = a²-b²

(a+b)³ = a³+b³+3ab(a+b)

(a-b)³ = a³-b³-3ab(a-b)

a³+b³ = (a+b)(a²+b²-ab)

a³-b³ = (a-b)(a²+b²+ab)

(a+b)² = (a-b)²+4ab

(a-b)² = (a+b)²-4ab

Answer 2

Answer:

The given expression is in the form of  a³ - b³ = ( a - b) (a² + ab + b²)

So we get

[ (x-2y) - (2x-y) ] [ (x-2y)² + (x-2y)(2x-y) + (2x-y)² ]

   = - (x + y) [ 7 x² + 7 y² - 13 x y ]

--------------------------------------------

(x - 2 y)³ - (2 x - y)³  

 = x³ - 8 y³ - 6 x² y + 12 x y² - [8 x³ - y³ - 12 x² y + 6 x y² ]

 = - 7 x³ - 7 y³ + 6 x² y + 6 x y²