Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(100p^{8}-169x^2\)
2. \(36y^2-25s^{14}\)
3. \(256b^{10}-9\)
4. \(25b^2-70b+49\)
5. \(121a^{10}-176a^5+64\)
6. \(y^2-28y+196\)
7. \(p^2-25\)
8. \(81b^{16}-1\)
9. \(169b^{8}-25\)
10. \(121s^{10}-81x^2\)
11. \(a^2-10a+25\)
12. \(9b^{8}-48b^4x+64x^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(100p^{8}-169x^2=(10p^4+13x)(10p^4-13x)\)
2. \(36y^2-25s^{14}=(6y-5s^7)(6y+5s^7)\)
3. \(256b^{10}-9=(16b^5+3)(16b^5-3)\)
4. \(25b^2-70b+49=(5b-7)^2\)
5. \(121a^{10}-176a^5+64=(11a^5-8)^2\)
6. \(y^2-28y+196=(y-14)^2\)
7. \(p^2-25=(p-5)(p+5)\)
8. \(81b^{16}-1=(9b^8+1)(9b^8-1)\)
9. \(169b^{8}-25=(13b^4+5)(13b^4-5)\)
10. \(121s^{10}-81x^2=(11s^5+9x)(11s^5-9x)\)
11. \(a^2-10a+25=(a-5)^2\)
12. \(9b^{8}-48b^4x+64x^2=(3b^4-8x)^2\)