Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(169-256q^{10}\)
2. \(25x^2-36a^{14}\)
3. \(p^2+16p+64\)
4. \(25q^{8}-140q^4+196\)
5. \(25-196q^{4}\)
6. \(s^2-28s+196\)
7. \(b^2+26b+169\)
8. \(121a^{10}-220a^5b+100b^2\)
9. \(16s^{6}+120s^3+225\)
10. \(144p^2-264p+121\)
11. \(s^2-169\)
12. \(169q^{4}+104q^2s+16s^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(169-256q^{10}=(13-16q^5)(13+16q^5)\)
2. \(25x^2-36a^{14}=(5x-6a^7)(5x+6a^7)\)
3. \(p^2+16p+64=(p+8)^2\)
4. \(25q^{8}-140q^4+196=(5q^4-14)^2\)
5. \(25-196q^{4}=(5-14q^2)(5+14q^2)\)
6. \(s^2-28s+196=(s-14)^2\)
7. \(b^2+26b+169=(b+13)^2\)
8. \(121a^{10}-220a^5b+100b^2=(11a^5-10b)^2\)
9. \(16s^{6}+120s^3+225=(4s^3+15)^2\)
10. \(144p^2-264p+121=(12p-11)^2\)
11. \(s^2-169=(s-13)(s+13)\)
12. \(169q^{4}+104q^2s+16s^2=(13q^2+4s)^2\)