Question

factorise using appropriate identity

Answer 1

4x²-8x+4-4y²

=> (4x²-8x+4)-4y²

=> [(2x)²+(2)²-2(2x)(2)]-(2y)²

=> using identity (a²+b²-2ab) = (a-b)²

=> (2x-2)²-(2y)²

=> using identity a²-b² = (a+b)(a-b)

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

=> [2(x-1+y)][2(x-1-y)]

=> 4(x+y-1)(x-y-1)


hope this helps

Answer 2

Heya user
Here is your answer !!

____________

( a - b )^2 = a^2 - 2ab + b^2
and
a^2 - b^2 = ( a - b )( a + b )

Now ,factorising the term ,

4x^2 - 8x + 4 - 4y^2
= { ( 2x )^2 - ( 2 × 2x × 2 ) + ( 2 )^2 } - 4y^2
= ( 2x - 2 )^2 - ( 2y )^2
= ( 2x - 2 - 2y ) ( 2x - 2 + 2y )
= 2 * 2 ( x - 1 - y ) ( x - 1 + y )
= 4 ( x - 1 - y ) ( x - 1 + y ) . [ Answer ] .

____________

Hope it helps !!