Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(9y^{10}+60y^5+100\)
2. \(25-196p^{4}\)
3. \(169-196b^{14}\)
4. \(169b^2+26b+1\)
5. \(q^2-28q+196\)
6. \(4b^{4}+12b^2+9\)
7. \(4a^{10}+4a^5+1\)
8. \(169a^{6}+364a^3+196\)
9. \(100y^2-60y+9\)
10. \(p^2+10p+25\)
11. \(144p^2-1\)
12. \(196x^2+28x+1\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(9y^{10}+60y^5+100=(3y^5+10)^2\)
2. \(25-196p^{4}=(5-14p^2)(5+14p^2)\)
3. \(169-196b^{14}=(13-14b^7)(13+14b^7)\)
4. \(169b^2+26b+1=(13b+1)^2\)
5. \(q^2-28q+196=(q-14)^2\)
6. \(4b^{4}+12b^2+9=(2b^2+3)^2\)
7. \(4a^{10}+4a^5+1=(2a^5+1)^2\)
8. \(169a^{6}+364a^3+196=(13a^3+14)^2\)
9. \(100y^2-60y+9=(10y-3)^2\)
10. \(p^2+10p+25=(p+5)^2\)
11. \(144p^2-1=(12p+1)(12p-1)\)
12. \(196x^2+28x+1=(14x+1)^2\)