Odpowiedź:
Szczegółowe wyjaśnienie:
Korzystamy ze wzoru:
[tex](a-b)^{3} =a^{3} -3a^{2} b+3ab^{2} -b^{3}[/tex]
[tex]a=2[/tex] [tex]b=5x[/tex]
[tex](2-5x)^{3} =2^{3} -3*2^{2} *5x +3*2*(5x)^{2} -(5x)^{3} =[/tex]
[tex]=8 -3*4*5x+3*2*25x^{2} -125x^{3} =[/tex]
[tex]=8 -60x+150x^{2} -125x^{3}[/tex]
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Korzystamy ze wzoru:
[tex](a+b)^{3} =a^{3} +3a^{2}b+3ab^{2} +b^{3}[/tex]
[tex]a=3[/tex] [tex]b=\sqrt{2}[/tex]
[tex](3+\sqrt{2} )^{3} =3^{3} +3*3^{2} *\sqrt{2} +3*3*(\sqrt{2})^{2} +(\sqrt{2} )^{3} =[/tex]
[tex]=27+3*9*\sqrt{2} +9*2+\sqrt{2*2*2} =[/tex]
[tex]=27+27\sqrt{2} +18+\sqrt{4} *\sqrt{2} =[/tex]
[tex]=27+27\sqrt{2} +18+2\sqrt{2} =45+29\sqrt{2}[/tex]
