Question

How can we write
(1+yx)²+(y–x)²=(1+x²)(1+y²) ?

Answer 1

Step-by-step explanation:

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

${(1 + yx)}^{2} + (y - x)^{2} = 1 + {y}^{2} {x}^{2} +$

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

Using the above formula we can come to this conclusion.

${(1 + yx)}^{2} + {(y - x)}^{2} =1 + {y}^{2} {x}^{2} + {y}^2$

$+ {x}^{2} = (1 + {x}^{2}) + {y}^{2}(1 + {x}^{2}) =$

$(1 + {y}^{2})(1 + {x}^{2})$

Hence proved. Hope it helps you.