Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(196b^{4}+84b^2+9\)
2. \(81a^2-234a+169\)
3. \(196p^{8}+364p^4+169\)
4. \(9y^{4}-30y^2+25\)
5. \(p^2-30p+225\)
6. \(121b^2+198b+81\)
7. \(-225q^2+16\)
8. \(81p^{8}+18p^4q+1q^2\)
9. \(25a^{8}-140a^4p+196p^2\)
10. \(196s^{4}-252s^2+81\)
11. \(49q^{10}+154q^5+121\)
12. \(169x^2-100q^{10}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(196b^{4}+84b^2+9=(14b^2+3)^2\)
2. \(81a^2-234a+169=(9a-13)^2\)
3. \(196p^{8}+364p^4+169=(14p^4+13)^2\)
4. \(9y^{4}-30y^2+25=(3y^2-5)^2\)
5. \(p^2-30p+225=(p-15)^2\)
6. \(121b^2+198b+81=(11b+9)^2\)
7. \(-225q^2+16=(4-15q)(4+15q)\)
8. \(81p^{8}+18p^4q+1q^2=(9p^4+q)^2\)
9. \(25a^{8}-140a^4p+196p^2=(5a^4-14p)^2\)
10. \(196s^{4}-252s^2+81=(14s^2-9)^2\)
11. \(49q^{10}+154q^5+121=(7q^5+11)^2\)
12. \(169x^2-100q^{10}=(13x-10q^5)(13x+10q^5)\)