Question

(x+y)sgure - (x -y) sgure = ................​

Answer 1

Step-by-step explanation:

(x+y)

2

−(x−y)

2

=4xy , verified.

Step-by-step explanation:

We have,

(x+y)^2-(x-y)^2=4xy(x+y)

2

−(x−y)

2

=4xy

Verify, (x+y)^2-(x-y)^2=4xy(x+y)

2

−(x−y)

2

=4xy

L.H.S.=(x+y)^2-(x-y)^2=(x+y)

2

−(x−y)

2

Using algebraic identity,

(a+b)^{2}=a^{2}+b^{2}+2ab(a+b)

2

=a

2

+b

2

+2ab and

(a-b)^{2}=a^{2}+b^{2}-2ab(a−b)

2

=a

2

+b

2

−2ab

=(x^{2}+y^{2}+2xy)-(x^{2}+y^{2}-2xy)=(x

2

+y

2

+2xy)−(x

2

+y

2

−2xy)

=x^{2}+y^{2}+2xy-x^{2}-y^{2}+2xy=x

2

+y

2

+2xy−x

2

−y

2

+2xy

=2xy+2xy=2xy+2xy

= 4xy

= R.H.S., verified.

Hence, (x+y)^2-(x-y)^2=4xy(x+y)

2

−(x−y)

2

=4xy , verified.

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