Question

What is (x + y)2

+ (x – y)2 ? Also compute (x + y)2

– (x – y)2​

Answer 1

Step-by-step explanation:

${(x + y)}^{2} + {(x - y)}^{2} \\ = ( {x}^{2} + 2xy + {y}^{2} ) + ({x}^{2} - 2xy + {y}^{2} ) \\ = {x}^{2} + 2xy + {y}^{2} + {x}^{2} - 2xy + {y}^{2} \\ = 2 {x}^{2} + 2 {y}^{2} \\ = 2( {x}^{2} + {y}^{2} ) \\ \\ {(x + y)}^{2} - {(x - y)}^{2} \\ = ( {x}^{2} + 2xy + {y}^{2} ) - ( {x}^{2} - 2xy + {y}^{2} ) \\ = {x}^{2} + 2xy + {y}^{2} - {x}^{2} + 2xy - {y}^{2} \\ = 4xy$

Hope you get your answer