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The first box will be filled with [tex]x^2-2xy[/tex]Th second box will filled with [tex]x^2+2xy[/tex]The third box will be filled with [tex](x+y)^2[/tex]Step-by-step explanation:Given polynomial indentity is:[tex](x-y)^2+4xy=(x+y)^2[/tex]we will prove the identity one by one So,The first step is to open the (x-y)^2[tex]x^2-2xy+y^2+4xy=(x+y)^2[/tex]Combining like terms[tex]x^2-2xy+4xy+y^2=(x+y)^2\\x^2+2xy+y^2=(x+y)^2\\[/tex]Closing the formula[tex](x+y)^2=(x+y)^2[/tex]Considering the above proofThe first box will be filled with [tex]x^2-2xy[/tex]Th second box will filled with [tex]x^2+2xy[/tex]The third box will be filled with [tex](x+y)^2[/tex]Keywords: Polynomial identities, ExpressionsLearn more about polynomial identities at:brainly.com/question/10081622brainly.com/question/10341324#LearnwithBrainly