Question

Show that (x+y)² − (x −y)² = 4xy for all real numbers x and y.

Answer 1

To show: (x+y)² − (x −y)² = 4xy

Using difference of square identity:

`a^2-b^2=(a-b)(a+b)`

Taking left side

`\Rightarrow (x+y)^2-(x-y)^2`

`a\rightarrow x+y`

`b\rightarrow x-y`

`\Rightarrow (x+y+x-y)(x+y-x+y)`

`\Rightarrow (2x)(2y)`

`\Rightarrow 4xy`

hence proved

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