1. a) [latex](a+b)^2=a^2+2ab+b^2[/latex] b) [latex](sqrt3+2)^2=(sqrt3)^2+2 cdot sqrt3 cdot 2+2^2=3+4 sqrt{3}+4=7+4 sqrt{3}[/latex] ================ 2. a) [latex](a-b)^2=a^2-2ab+b^2[/latex] b) [latex](2sqrt2-3)^2=(2sqrt2)^2-2 cdot 2sqrt2 cdot 3+3^2=8-12sqrt2 +9=17-12sqrt2[/latex] ================ 3. a) [latex](a+b)(a-b)=a^2-b^2[/latex] b) [latex](0,3-x^2)(0,3+x^2)=(0,3)^2-(x^2)^2=0,09-x^4[/latex] ================ 4. a) [latex]a^3-b^3=(a - b)(a^2 + ab + b^2)[/latex] b) [latex]27-x^3=3^3-x^3=(3-x)(3^2+3x+x^2)=(3-x)(9+3x+x^2)[/latex] ================ 5. a) [latex]x^3+64=0[/latex] [latex]x^3+4^3=0[/latex] [latex](x + 4)(x^2 - 4x + 16)=0[/latex] [latex]x + 4=0[/latex] [latex]x=-4[/latex] b) [latex]x^3+6x^2+9x=0[/latex] [latex]x(x^2+6x+9)=0[/latex] [latex]x(x+3)^2=0[/latex] [latex]x=0 lub (x+3)^2=0[/latex] [latex]. x+3=0[/latex] [latex]. x=-3[/latex] c) [latex]x^2(x-2)(2x+3)(x+7)=0[/latex] [latex]x^2=0 lub x-2=0 lub 2x+3=0 lub x+7=0[/latex] [latex]x=0 lub x=2 lub 2x=-3 /:2 lub x=-7[/latex] [latex]. x=-1,5[/latex]
