Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(100p^{6}-180p^3x+81x^2\)
2. \(64p^{4}+176p^2s+121s^2\)
3. \(a^{4}-100q^2\)
4. \(81p^{8}+252p^4+196\)
5. \(100a^{4}+20a^2s+1s^2\)
6. \(49s^{14}-16x^2\)
7. \(100s^2-260s+169\)
8. \(16b^{6}-88b^3+121\)
9. \(196-169b^{6}\)
10. \(121b^2-352b+256\)
11. \(-225p^2+64\)
12. \(64p^2+48p+9\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(100p^{6}-180p^3x+81x^2=(10p^3-9x)^2\)
2. \(64p^{4}+176p^2s+121s^2=(8p^2+11s)^2\)
3. \(a^{4}-100q^2=(a^2+10q)(a^2-10q)\)
4. \(81p^{8}+252p^4+196=(9p^4+14)^2\)
5. \(100a^{4}+20a^2s+1s^2=(10a^2+s)^2\)
6. \(49s^{14}-16x^2=(7s^7+4x)(7s^7-4x)\)
7. \(100s^2-260s+169=(10s-13)^2\)
8. \(16b^{6}-88b^3+121=(4b^3-11)^2\)
9. \(196-169b^{6}=(14-13b^3)(14+13b^3)\)
10. \(121b^2-352b+256=(11b-16)^2\)
11. \(-225p^2+64=(8-15p)(8+15p)\)
12. \(64p^2+48p+9=(8p+3)^2\)