Rozłóż na czynniki pierwsze. Zadania w załączniku, bardzo proszę o pomoc.

rozwiązanie w załączniku ( mam nadzieję, że pod koniec nic nie namieszałam. ;) )

[latex]x^2+2x+1=(x+1)^2[/latex] --- [latex]x^2-4x+4=(x-2)^2[/latex] --- [latex]4x^2+8xy+4y^2=4(x+y)^2[/latex] --- [latex]a^2-10ab+25b^2=(a-5b)^2[/latex] --- [latex]x^2+6x+9=(x+3)^2[/latex] --- [latex]25x^2-20x+4=(5x-2)^2[/latex] --- [latex]x^2-25=(x-5)(x+5)[/latex] --- [latex]x^2-3=(x-sqrt{3})(x+sqrt{3})[/latex] --- [latex]4x^2-1=(2x-1)(2x+1)[/latex] --- [latex]9-2x^2=(3-xsqrt{2})(3+xsqrt{2})[/latex] --- [latex]x^2-y^2=(x-y)(x+y)[/latex] --- [latex]2x^2-3y^2=(xsqrt{2}-ysqrt{3})(xsqrt{2}+ysqrt{3})[/latex] --- [latex]2x-2=2(x-1)[/latex] --- [latex]x^2-x=x(x-1)[/latex] --- [latex]5x^2-10x=5x(x-2)[/latex] --- [latex]x^3-9x=x(x^2-9)=x(x-3)(x+3)[/latex] --- [latex]x^2+4x+4=(x+2)^2[/latex] --- [latex]x^4-x^3-x^2=x^2(x^2-x-1)=x^2(x-dfrac{1-sqrt{5}}{2})(x-dfrac{1+sqrt{5}}{2})[/latex] --- [latex]x^2(x-3)+9(x-3)=(x^2+9)(x-3)[/latex] --- [latex](x^2-2)(x+2)-2(x+2)=(x^2-4)(x+2)=(x-2)(x+2)^2[/latex] --- [latex](a+3b)^2-(a-3b)^2=(a+3b-(a-3b))(a+3b+(a-3b))=6bcdot 2a=12ab[/latex]