Question

Proszę o pomoc!! Zastosować wzory skróconego mnożenia

Answer 1

Przypomnijmy sobie wzory skróconego mnożenia:

Wzór na kwadrat sumy:

[tex]\huge{\boxed{(a+b)^2 = a^2 +2ab+b^2}}[/tex]

Wzór na kwadrat różnicy:

[tex]\huge{\boxed{(a-b)^2=a^2-2ab+b^2}}[/tex]

Wzór na różnicę kwadratów:

[tex]\huge{\boxed{a^2-b^2=(a-b)(a+b)}}[/tex]

Rozwiązujemy przykłady:

[tex]a) \ \ (\sqrt{2}+2)^2 = (\sqrt{2})^2+2 \cdot \sqrt{2} \cdot 2 + 2^2 = 2 + 4 \sqrt{2} + 4 = \large\boxed{6+4\sqrt{2} }}[/tex]

[tex]b) \ \ (3+2\sqrt{3} )^2=3^2 +2 \cdot 3 \cdot 2\sqrt{3} + (2\sqrt{3})^2=9+12\sqrt{3} + 12 = \large{\boxed{21 + 12\sqrt{3} }}[/tex]

[tex]c) \ \ (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+ 48\sqrt{3} + 24 = \large{\boxed{96 + 48\sqrt{3} }}[/tex]

[tex]d) \ \ (\sqrt{2}-4)^2 = (\sqrt{2})^2-2 \cdot \sqrt{2} \cdot 4 +4^2 = 2-8\sqrt{2} +16=\large{\boxed{18-8\sqrt{2}}}[/tex]

[tex]e) \ \ (\sqrt{2}-\sqrt{3})^2 = (\sqrt{2})^2-2 \cdot \sqrt{2} \cdot \sqrt{3} + (\sqrt{3})^2 = 2 - 2\sqrt{6} +3 = \large{\boxed{5-2\sqrt{6} }}[/tex]

[tex]f) \ \ (2\sqrt{10} - 5\sqrt{2} )^2 = (2\sqrt{10})^2-2 \cdot 2\sqrt{10} \cdot 5\sqrt{2} +(5\sqrt{2})^2 = 40 - 40\sqrt{5} + 50 = \large{\boxed{90 -40\sqrt{5} }}[/tex]

[tex]g) \ \ (\sqrt{3} -1)(\sqrt{3} +1) = (\sqrt{3} )^2-1^2 = 3-1 = \large{\boxed{2}}[/tex]

[tex]h) \ \ (3+\sqrt{7} )(\sqrt{7}-3) =(\sqrt{7} -3 )(\sqrt{7}+3)=(\sqrt{7})^2-3^2=7-9=\large{\boxed{-2}}[/tex]

[tex]i) \ \ (1+4\sqrt{5})(1-4\sqrt{5})=1^2 -(4\sqrt{5})^2=1-80=\large{\boxed{-79}}[/tex]