Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(-256x^2+9\)
2. \(121x^{4}-286x^2y+169y^2\)
3. \(4p^2-25\)
4. \(169s^{4}+26s^2y+1y^2\)
5. \(196p^2-364p+169\)
6. \(81a^2-234a+169\)
7. \(100q^{10}-180q^5+81\)
8. \(121-9p^{14}\)
9. \(121y^2-64s^{6}\)
10. \(25b^{12}-1\)
11. \(4y^{6}+4y^3+1\)
12. \(b^2-28b+196\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(-256x^2+9=(3-16x)(3+16x)\)
2. \(121x^{4}-286x^2y+169y^2=(11x^2-13y)^2\)
3. \(4p^2-25=(2p+5)(2p-5)\)
4. \(169s^{4}+26s^2y+1y^2=(13s^2+y)^2\)
5. \(196p^2-364p+169=(14p-13)^2\)
6. \(81a^2-234a+169=(9a-13)^2\)
7. \(100q^{10}-180q^5+81=(10q^5-9)^2\)
8. \(121-9p^{14}=(11-3p^7)(11+3p^7)\)
9. \(121y^2-64s^{6}=(11y-8s^3)(11y+8s^3)\)
10. \(25b^{12}-1=(5b^6+1)(5b^6-1)\)
11. \(4y^{6}+4y^3+1=(2y^3+1)^2\)
12. \(b^2-28b+196=(b-14)^2\)