Hej! Spiesze z pomoca :D
[tex]12. \\(\frac15-\frac13d)^2=(\frac15)^2-2*\frac15*\frac13d+(\frac13d)^2=\frac1{25}-\frac2{15}d+\frac19d^2[/tex]
[tex]13. \\(\sqrt{d}-6)(\sqrt{d}+6)=(\sqrt{d})^2-6^2=d-36[/tex]
[tex]14. \\(3\sqrt{k}-6)^2=(3\sqrt{k})^2-2*3\sqrt{k}*6+6^2=9k-6\sqrt{k}+36[/tex]
[tex]15. \\(\sqrt{a}+1)^2=(\sqrt{a})^2+2*\sqrt{a}*1+1^2=a+2\sqrt{a}+1[/tex]
[tex]16. \\(13+5\sqrt{b})(13-5\sqrt{5})=13^2-(5\sqrt{b})^2=169-25b[/tex]
[tex]17. \\(8p^2-12)(12+8p^2)=(8p^2-12)(8p^2+12)=(8p^2)^2-12^2=64p^4-144[/tex]
[tex]18. \\(\frac12y^2-xz)(\frac12y^2+xz)=(\frac12y^2)^2-(xz)^2=\frac12y^4-x^2z^2[/tex]
[tex]19. \\(12w^2+14)^2=(12w^2)^2+2*12w^2*14+14^2=144w^4+336w^2+196[/tex]
[tex]20. \\(20-5c^4)^2=20^2-2*20*5c^4+(5c^4)^2=400-200c^4+25c^8[/tex]
[tex]21. \\(-3a+5s)^2=(-3a)^2+2*(-3a)*5s+(5s)^2=9a^2-30as+25s^2[/tex]
[tex]22. \\(4-3xy)(3xy+4)=(4-3xy)(4+3xy)=4^2-(3xy)^2=16-9x^2y^2[/tex]
[tex]23. \\(\sqrt{\sqrt3+x}+\sqrt{\sqrt3-x})^2=(\sqrt{\sqrt3+x})^2+2*\sqrt{\sqrt3+x}*\sqrt{\sqrt3-x}+(\sqrt{\sqrt3-x})^2=\sqrt3+x+2\sqrt{(\sqrt3+x)(\sqrt3-x)}+\sqrt3-x=2\sqrt3+2\sqrt{(\sqrt3)^2-x^2}=2\sqrt3+2\sqrt{9-x^2}[/tex]
Wykorzystane wzory i zaleznosci:
[tex](a+b)^2=a^2+2ab+b^2\\(a-b)^2=a^2-2ab+b^2\\(a-b)(a+b)=a^2-b^2\\\sqrt{a}*\sqrt{b}=\sqrt{ab}\\(a^x)^y=a^{xy}[/tex]
