Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(25p^{16}-4s^2\)
2. \(p^2-225\)
3. \(196x^2+308x+121\)
4. \(196x^{8}+252x^4+81\)
5. \(225a^{10}+390a^5y+169y^2\)
6. \(p^2-81\)
7. \(49a^{10}-84a^5q+36q^2\)
8. \(q^2-16q+64\)
9. \(4b^{10}+36b^5+81\)
10. \(49-121b^{10}\)
11. \(4x^2-81b^{8}\)
12. \(169q^{16}-16\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(25p^{16}-4s^2=(5p^8+2s)(5p^8-2s)\)
2. \(p^2-225=(p-15)(p+15)\)
3. \(196x^2+308x+121=(14x+11)^2\)
4. \(196x^{8}+252x^4+81=(14x^4+9)^2\)
5. \(225a^{10}+390a^5y+169y^2=(15a^5+13y)^2\)
6. \(p^2-81=(p+9)(p-9)\)
7. \(49a^{10}-84a^5q+36q^2=(7a^5-6q)^2\)
8. \(q^2-16q+64=(q-8)^2\)
9. \(4b^{10}+36b^5+81=(2b^5+9)^2\)
10. \(49-121b^{10}=(7-11b^5)(7+11b^5)\)
11. \(4x^2-81b^{8}=(2x-9b^4)(2x+9b^4)\)
12. \(169q^{16}-16=(13q^8+4)(13q^8-4)\)