Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(81y^2-16x^{10}\)
2. \(25b^{4}+90b^2y+81y^2\)
3. \(169a^{10}-78a^5s+9s^2\)
4. \(225-64a^{16}\)
5. \(169q^{6}-130q^3+25\)
6. \(196p^{12}-121s^2\)
7. \(p^2-10p+25\)
8. \(-121s^2+144\)
9. \(36s^{4}+132s^2+121\)
10. \(-121s^2+81\)
11. \(4q^2+60q+225\)
12. \(49y^2-100x^{16}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(81y^2-16x^{10}=(9y-4x^5)(9y+4x^5)\)
2. \(25b^{4}+90b^2y+81y^2=(5b^2+9y)^2\)
3. \(169a^{10}-78a^5s+9s^2=(13a^5-3s)^2\)
4. \(225-64a^{16}=(15-8a^8)(15+8a^8)\)
5. \(169q^{6}-130q^3+25=(13q^3-5)^2\)
6. \(196p^{12}-121s^2=(14p^6+11s)(14p^6-11s)\)
7. \(p^2-10p+25=(p-5)^2\)
8. \(-121s^2+144=(12-11s)(12+11s)\)
9. \(36s^{4}+132s^2+121=(6s^2+11)^2\)
10. \(-121s^2+81=(9-11s)(9+11s)\)
11. \(4q^2+60q+225=(2q+15)^2\)
12. \(49y^2-100x^{16}=(7y-10x^8)(7y+10x^8)\)