Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(121-169x^{16}\)
2. \(4b^{4}+52b^2y+169y^2\)
3. \(25b^{10}-120b^5+144\)
4. \(256q^{16}-25y^2\)
5. \(49p^{8}-126p^4+81\)
6. \(a^2-30a+225\)
7. \(144b^{8}-264b^4y+121y^2\)
8. \(q^2-9\)
9. \(p^2-225\)
10. \(169b^{10}-225\)
11. \(-36y^2+25\)
12. \(256x^{4}-480x^2+225\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(121-169x^{16}=(11-13x^8)(11+13x^8)\)
2. \(4b^{4}+52b^2y+169y^2=(2b^2+13y)^2\)
3. \(25b^{10}-120b^5+144=(5b^5-12)^2\)
4. \(256q^{16}-25y^2=(16q^8+5y)(16q^8-5y)\)
5. \(49p^{8}-126p^4+81=(7p^4-9)^2\)
6. \(a^2-30a+225=(a-15)^2\)
7. \(144b^{8}-264b^4y+121y^2=(12b^4-11y)^2\)
8. \(q^2-9=(q+3)(q-3)\)
9. \(p^2-225=(p+15)(p-15)\)
10. \(169b^{10}-225=(13b^5+15)(13b^5-15)\)
11. \(-36y^2+25=(5-6y)(5+6y)\)
12. \(256x^{4}-480x^2+225=(16x^2-15)^2\)