Răspuns:
[tex]\displaystyle{ = -2x^{2} - 25y^{2} - 15xy }[/tex]
Explicație pas cu pas:
[tex]\displaystyle{ (x + 2y) \cdot (x + y) = x \cdot x + x \cdot y + 2y \cdot x + 2y \cdot y }[/tex]
[tex]\displaystyle{ = x^{2} + xy + 2xy + 2y^{2} }[/tex]
[tex]\displaystyle{ = x^{2} + 2y^{2} + 3xy }[/tex]
[tex]\displaystyle{ (x\sqrt{3} + y\sqrt{27})^{2} = (x\sqrt{3} + 3y\sqrt{3} )^{2} }[/tex]
[tex]\displaystyle{ = [\sqrt{3} \cdot (x + 3y)]^{2} }[/tex]
[tex]\displaystyle{ = (\sqrt{3})^{2} \cdot (x + 3y)^{2} }[/tex]
[tex]\displaystyle{ = 3 \cdot (x^{2} + 6xy + 9y^{2}) }[/tex]
[tex]\displaystyle{ = 3x^{2} + 18xy + 27y^{2} }[/tex]
[tex]\displaystyle{ (x + 2y) \cdot (x+ y) - (x\sqrt{3} + y\sqrt{27})^{2} = x^{2} + 2y^{2} + 3xy - (3x^{2} + 18xy + 27y^{2}) }[/tex]
[tex]\displaystyle{ = x^{2} + 2y^{2} + 3xy - 3x^{2} - 18xy - 27y^{2} }[/tex]
[tex]\displaystyle{ = -2x^{2} - 25y^{2} - 15xy }[/tex]
