[tex]a. \\
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(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\\
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4xy=4*\frac12*3=2*3=6\\
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b. \\
x(x+2y)-(x+y)^2=x^2+2xy-(x^2+2xy+y^2)=x^2+2xy-x^2-2xy-y^2=-y^2\\
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-y^2=-(1\frac14)^2=-(\frac54)^2=-\frac{25}{16}[/tex]
[tex]c.\\
2(x-y)^2-(x+y)(x-y)+4xy=2(x^2-2xy+y^2)-(x^2-y^2)+4xy=2x^2-4xy+2y^2-x^2+y^2+4xy=x^2+3y^2\\
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x^2+3y^2=(\sqrt7)^2+3*(\sqrt6)^2=7+3*6=7+18=25\\
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d. \\
(a-4b)^2+(a-b)(a+16b)=a^2-8ab+16b^2+a^2+16ab-ab-16b^2=2a^2+7ab\\
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2a^2+7ab=2*(\sqrt2)^2+7*\sqrt2*\frac12=2*2+\frac72\sqrt2=4+\frac72\sqrt2=\frac82+\frac72\sqrt2=\frac{8+7\sqrt2}2[/tex]
