c) Folosim: (2√2)²=8
[tex]\underbrace{(x+\sqrt{2})^{2} - (2\sqrt{2})^{2}}_{(a-b)(a+b)} = (x+\sqrt{2}-2\sqrt{2})(x+\sqrt{2}+2\sqrt{2}) = (x-\sqrt{2})(x+3\sqrt{2})[/tex]
g) Avem √3²=3
[tex]\underbrace{x^{2}-2\cdot1\cdot\sqrt{3}x+(\sqrt{3})^{2}}_{(a-b)^2}-(y-2\sqrt{3})^{2} = \underbrace{(x-\sqrt{3})^{2}-(y-2\sqrt{3})^{2}}_{(a-b)(a+b)} = \\[/tex]
[tex]= \Big[x-\sqrt{3}-(y-2\sqrt{3})\Big] \cdot \Big[x-\sqrt{3}+(y-2\sqrt{3})\Big]\\[/tex]
[tex]= \Big(x-\sqrt{3}-y+2\sqrt{3}\Big) \cdot \Big(x-\sqrt{3}+y-2\sqrt{3}\Big)\\[/tex]
[tex]= \Big(x-y+\sqrt{3}\Big) \cdot \Big(x+y-3\sqrt{3}\Big)[/tex]
______
Formule de calcul prescurtat:
[tex]\boxed{\boxed{\boldsymbol{(a \pm b)^{2} = a^{2} \pm 2ab + b^{2}}} \ \ \boxed{\boldsymbol{(a - b)(a + b) = a^{2} - b^{2}}}}\\[/tex]
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c) Folosim: (2√2)²=8
[tex]\underbrace{(x+\sqrt{2})^{2} - (2\sqrt{2})^{2}}_{(a-b)(a+b)} = (x+\sqrt{2}-2\sqrt{2})(x+\sqrt{2}+2\sqrt{2}) = (x-\sqrt{2})(x+3\sqrt{2})[/tex]
g) Avem √3²=3
[tex]\underbrace{x^{2}-2\cdot1\cdot\sqrt{3}x+(\sqrt{3})^{2}}_{(a-b)^2}-(y-2\sqrt{3})^{2} = \underbrace{(x-\sqrt{3})^{2}-(y-2\sqrt{3})^{2}}_{(a-b)(a+b)} = \\[/tex]
[tex]= \Big[x-\sqrt{3}-(y-2\sqrt{3})\Big] \cdot \Big[x-\sqrt{3}+(y-2\sqrt{3})\Big]\\[/tex]
[tex]= \Big(x-\sqrt{3}-y+2\sqrt{3}\Big) \cdot \Big(x-\sqrt{3}+y-2\sqrt{3}\Big)\\[/tex]
[tex]= \Big(x-y+\sqrt{3}\Big) \cdot \Big(x+y-3\sqrt{3}\Big)[/tex]
______
Formule de calcul prescurtat:
[tex]\boxed{\boxed{\boldsymbol{(a \pm b)^{2} = a^{2} \pm 2ab + b^{2}}} \ \ \boxed{\boldsymbol{(a - b)(a + b) = a^{2} - b^{2}}}}\\[/tex]