Question

factorise using appropriate identities 1. 9x²+6xy+y²,
2.4y²-4y+1,
3.x²-y²/100

Answer 1

Hii there!!!

1) 9x^2 + 6xy + y^2

=> 9x^2 + 3xy + 3xy + y^2

=> 3x( 3x + y ) + y ( 3x + y )

=> ( 3x + y ) ( 3x + y )

OR

9x^2 + 6xy + y^2

=> ( 3x )^2 + 2( 3x )( y ) + ( y )^2

=> ( 3x + y )^2



2) 4y^2 - 4y + 1

=> 4y^2 - 2y - 2y + 1

=> 2y( 2y - 1 ) - 1( 2y - 1 )

=> ( 2y - 1 ) ( 2y - 1 )

OR

4y^2 - 4y + 1

=> ( 2y )^2 - ( 2 )( 2y )( 1 ) + ( 1 )^2

=> ( 2y - 1 )^2


3) x^2 - y^2/100

=> ( x )^2 - ( y/10 )^2

=> ( x + y/10 ) ( x - y/10 )

Hope it helps....

Answer 2

1. 9x² + 6xy + y²
=> (3x)² + 2 (3x)(y) + (y)²
=> (3x+y)²
=> (3x+y) (3x+y)

2. 4y² - 4y + 1
=> (2y)² - 2 (2y)(1) + (1)²
=> (2y - 1)²
=> (2y-1) (2y-1)

3. x² - y² / 100
=> (x - y/10) (x+y/10)