Basiskennis chemie 4/Tweedegraads (x+b)2 Opgaven

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Theorie

Theorie over dit onderwerp vind je hier.

Opgaven

(x + a)²

Aangenomen wordt dat je de kwadraten van 1 tot en met 10 uit je hoofd weet.
Ook kun je bijboorbeeld ${\ce {70^2}}$ berekenen via ${\ce {70^{2}\ =\ (7\times \ 10)^{2}\ =\ 7^{2}\times 10^{2}\ =\ 49\ \times 100\ =\ 4900}}$

Bereken zonder rekenmachine, een kladblaadje mag wel

1. ${\ce {21^2}}$ 441 ${\ce {21^2}}$ ${\ce {(20 \ + \ 1)^2}}$ ${\ce {20^{2}\ +\ 2\ \times \ 20\times \ 1\ +\ 1^{2}}}$ ${\ce {400 \ + \ 40 \ + \ 1 \ = \ 441}}$	2. ${\ce {63^2}}$ 3969 ${\ce {63^2}}$ ${\ce {(60 \ + \ 3)^2}}$ ${\ce {60^{2}\ +\ 2\ \times \ 60\times \ 3\ +\ 3^{2}}}$ ${\ce {3600 \ + \ 360 \ + \ 9 \ = \ 3969}}$	3. ${\ce {41^2}}$ 1681 ${\ce {41^2}}$ ${\ce {(40 \ + \ 1)^2}}$ ${\ce {40^{2}\ +\ 2\ \times \ 40\times \ 1\ +\ 1^{2}}}$ ${\ce {1600 \ + \ 80 \ + \ 1 \ = \ 1681}}$
4. ${\ce {19^2}}$ 361 ${\ce {19^2}}$ ${\ce {(20 \ - \ 1)^2}}$ ${\ce {20^{2}\ -\ 2\ \times \ 20\times \ 1\ +\ 1^{2}}}$ ${\ce {400 \ - \ 40 \ + \ 1 \ = \ 361}}$	5. ${\ce {38^2}}$ 1444 ${\ce {38^2}}$ ${\ce {(40 \ - \ 2)^2}}$ ${\ce {40^{2}\ -\ 2\ \times \ 40\times \ 2\ +\ 2^{2}}}$ ${\ce {1600 \ - \ 160 \ + \ 4 \ = \ 1444}}$	6. ${\ce {49^2}}$ 2401 ${\ce {49^2}}$ ${\ce {(50 \ - \ 1)^2}}$ ${\ce {50^{2}\ -\ 2\ \times \ 50\times \ 2\ +\ 1^{2}}}$ ${\ce {2500 \ - \ 100 \ + \ 1 \ = \ 2401}}$
7. ${\ce {98^2}}$ 9604 ${\ce {98^2}}$ ${\ce {(100 \ - \ 2)^2}}$ ${\ce {100^{2}\ -\ 2\ \times \ 100\times \ 2\ +\ 2^{2}}}$ ${\ce {10000 \ - \ 400 \ + \ 4 \ = \ 9604}}$	8. ${\ce {98^2}}$ 9604 ${\ce {101^2}}$ ${\ce {(100 \ + \ 1)^2}}$ ${\ce {100^{2}\ +\ 2\ \times \ 100\times \ 1\ +\ 1^{2}}}$ ${\ce {10000 \ + \ 200 \ + \ 1 \ = \ 10201}}$	9. ${\ce {112^2}}$ 12541 ${\ce {112^2}}$ ${\ce {(110 \ + \ 2)^2}}$ 1102 kun je zien als: ${\ce {(11\ \times \ 10)^{2}}}$ ${\ce {11^{2}=10^{2}\ +\ 2\ \times \ 10\ \times 1\ +\ 1^{2}\ =\ 100\ +\ 20\ +\ 1\ =\ 120}}$ zodat ${\ce {110^{2}\ =\ 11^{2}\ \times 10^{2}\ =\ 12100}}$ en ${\ce {110^{2}\ +\ 2\ \times \ 110\times \ 2\ +\ 2^{2}}}$ ${\ce {12100 \ + \ 440 \ + \ 1 \ = \ 12541}}$

(ax + b)²

Schrijf in een keer de uitkomst van de volgende kwadraten op

10. ${\ce {(a \ + \ 3)^2}}$ ${\ce {a^2 \ + \ 6a \ + \ 9}}$	11. ${\ce {(c \ + \ 7)^2}}$ ${\ce {c^2 \ + \ 14c \ + \ 49}}$	12. ${\ce {(x\ +\ b)^{2}}}$ ${\ce {x^{2}\ +\ 2bx\ +\ b^{2}}}$
13. ${\ce {(g \ - \ 8)^2}}$ ${\ce {g^2 \ - \ 16g \ + \ 64}}$	14. ${\ce {(d\ -\ y)^{2}}}$ ${\ce {d^{2}\ -\ 2dy\ +\ y^{2}}}$	15. ${\ce {(x \ - \ 3k)^2}}$ ${\ce {x^2 \ - \ 6kx \ + \ 9k^2}}$
16. ${\ce {(2x\ +\ b)^{2}}}$ ${\ce {4x^{2}\ +\ 4bx\ +\ b^{2}}}$	17. ${\ce {(5x \ + \ 2y)^2}}$ ${\ce {25x^2 \ + \ 20xy \ + \ 4y^2}}$	18. ${\ce {{\big (}{\frac {2}{3}}c\ +\ {\frac {1}{4}}{\big )}^{2}}}$ ${\ce {{\frac {4}{9}}c^2 \ + \ {\frac {1}{3}}c \ + \ {\frac {1}{16}}}}$

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