Question

Factorize 4(x-y) ^2 – 12(x – y)(x + y) + 9(x + y)^2​

Answer 1

Answer:

Given Equation is 4(x - y)^2 - 12(x - y)(x + y) + 9(x + y)^2

= > 4(x^2 - 2xy + y^2) - 12(x^2 - y^2) + 9(x^2 + y^2 + 2xy)

= > 4x^2 - 8xy + 4y^2 - 12x^2 + 12y^2 + 9x^2 + 9y^2 + 18xy

= > x^2 + 10xy + 25y^2

= > x^2 + 5xy + 5xy + 25y^2

= > x(x + 5y) + 5y(x + 5y)

= > (x + 5y)(x + 5y)

= > (x + 5y)^2.

Therefore, Factorization of 4(x - y)^2 - 12(x - y)(x + y) + 9(x + y)^2 = (x + 5y)^2.

Hope this helps!

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Answer 2

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Consider ( x – y ) = p, ( x + y ) = q

= 4p^2 – 12pq + 9q^2

Expanding the middle term,

-12 = -6 -6

also 4× 9=-6 × -6

= 4p^2 – 6pq – 6pq + 9q^2

=2p( 2p – 3q ) -3q( 2p – 3q )

= ( 2p – 3q ) ( 2p – 3q )

= ( 2p – 3q )^2

Substituting back

p = x – y and q = x + y;

= [2( x-y ) – 3( x+y)]^2

 = [ 2x – 2y – 3x – 3y ]^2

= (2x-3x-2y-3y )^2

=[ -x – 5y]^2

=[( -1 )( x+5y )]^2

=( x+5y )^2

Therefore,

4(x-y)^2 – 12(x – y)(x + y) + 9(x + y)^2 

= ( x+5y )^2