To show: (x+y)² − (x −y)² = 4xy
Using difference of square identity:
[tex]a^2-b^2=(a-b)(a+b)[/tex]
Taking left side
[tex]\Rightarrow (x+y)^2-(x-y)^2[/tex]
[tex]a\rightarrow x+y[/tex]
[tex]b\rightarrow x-y[/tex]
[tex]\Rightarrow (x+y+x-y)(x+y-x+y)[/tex]
[tex]\Rightarrow (2x)(2y)[/tex]
[tex]\Rightarrow 4xy[/tex]
hence proved
[tex](x+y)^2-(x-y)^2=4xy[/tex]
