Cześć!
a)
[tex](4\sqrt2-8)(4\sqrt2+8)=(4\sqrt2)^2-8^2=4^2\cdot(\sqrt2)^2-64=\\\\=16\cdot2-64=32-64=\boxed{-32}[/tex]
b)
[tex](5\sqrt3+4)^2=(5\sqrt3)^2+2\cdot5\sqrt3\cdot4+4^2=\\\\=5^2\cdot(\sqrt3)^2+40\sqrt3+16=25\cdot3+40\sqrt3+16=75+40\sqrt3+16=\boxed{91+40\sqrt3}[/tex]
c)
[tex](8-3\sqrt3)^2=8^2-2\cdot8\cdot3\sqrt3+(3\sqrt3)^2=\\\\=64-48\sqrt3+3^2\cdot(\sqrt3)^2=64-48\sqrt3+9\cdot3=64-48\sqrt3+27=\boxed{91-48\sqrt3}[/tex]
d)
[tex](\sqrt2+3\sqrt5)^2=(\sqrt2)^2+2\cdot\sqrt2\cdot3\sqrt5+(3\sqrt5)^2=\\\\=2+6\sqrt{10}+3^2\cdot(\sqrt5)^2=2+6\sqrt{10}+9\cdot5=2+6\sqrt{10}+45=\boxed{47+6\sqrt{10}}[/tex]
Wykorzystane wzory skróconego mnożenia
[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[/tex]
