Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(100p^{16}-49x^2\)
2. \(100q^2-49b^{4}\)
3. \(169x^{12}-9\)
4. \(s^2+18s+81\)
5. \(9b^{8}-84b^4p+196p^2\)
6. \(121a^{6}+330a^3+225\)
7. \(25-4b^{14}\)
8. \(144q^{8}+24q^4+1\)
9. \(81x^2+18x+1\)
10. \(-36x^2+121\)
11. \(-9p^2+49\)
12. \(144-121s^{14}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(100p^{16}-49x^2=(10p^8+7x)(10p^8-7x)\)
2. \(100q^2-49b^{4}=(10q-7b^2)(10q+7b^2)\)
3. \(169x^{12}-9=(13x^6+3)(13x^6-3)\)
4. \(s^2+18s+81=(s+9)^2\)
5. \(9b^{8}-84b^4p+196p^2=(3b^4-14p)^2\)
6. \(121a^{6}+330a^3+225=(11a^3+15)^2\)
7. \(25-4b^{14}=(5-2b^7)(5+2b^7)\)
8. \(144q^{8}+24q^4+1=(12q^4+1)^2\)
9. \(81x^2+18x+1=(9x+1)^2\)
10. \(-36x^2+121=(11-6x)(11+6x)\)
11. \(-9p^2+49=(7-3p)(7+3p)\)
12. \(144-121s^{14}=(12-11s^7)(12+11s^7)\)