I tutaj znowu mamy piękny wzór skróconego mnożenia. [latex](a+b)^2=(a+b)cdot (a+b) = a^2+ab+ba=b^2=a^2+2ab+b^2[/latex] i tutaj drobna uwaga: [latex]abcdot ab = a^2 cdot b^2[/latex] nie mylić z [latex]ab+ab=2ab[/latex] a) [latex](2 sqrt{5}+3 sqrt{7} )^2= (2 sqrt{5} )^2+2cdot 2 sqrt{5} cdot 3 sqrt{7} + (3 sqrt{7} )^2= 20+12 sqrt{35} +63=83+12sqrt{35}.[/latex] b) [latex](4 sqrt{3}+5 sqrt{2} )^2= (4 sqrt{3} )^2 + 2cdot 4 sqrt{3} cdot 5 sqrt{2} + (5 sqrt{2} )^2=48+40 sqrt{6} + 50=98+40sqrt{6}.[/latex] c) [latex](6 sqrt{2}+2 sqrt{6} )^2 = (6 sqrt{2} )^2 + 2 cdot 6 sqrt{2} cdot 2 sqrt{6}+(2 sqrt{6} )^2 = 72+24 sqrt{12} + 24[/latex]=[latex]96+24 sqrt{4cdot 3} = 96+24 sqrt{4} cdot sqrt{3} = 96+48 sqrt{3} .[/latex] d) [latex](7 sqrt{2}+3 sqrt{10} )^2 = (7 sqrt{2} )^2+ 2 cdot 7 sqrt{2} cdot 3 sqrt{10} +(3 sqrt{10} )^2=98+42 sqrt{20} + [/latex] [latex]90=188+42 sqrt{4cdot 5}= 188+42cdot sqrt{4} cdot sqrt{5} =188+84 sqrt{5}. [/latex] Mała uwaga: [latex]a sqrt{b} [/latex] to jest to samo co [latex]acdot sqrt{b}. [/latex]
