Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(9b^{8}-48b^4+64\)
2. \(169a^{10}-16\)
3. \(4p^{4}+4p^2+1\)
4. \(49a^{8}-42a^4+9\)
5. \(144a^{10}-168a^5p+49p^2\)
6. \(25y^2-144\)
7. \(225-64b^{10}\)
8. \(s^2-225\)
9. \(s^2-6s+9\)
10. \(64s^{10}-240s^5y+225y^2\)
11. \(121b^{10}-286b^5x+169x^2\)
12. \(p^{12}-100x^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(9b^{8}-48b^4+64=(3b^4-8)^2\)
2. \(169a^{10}-16=(13a^5+4)(13a^5-4)\)
3. \(4p^{4}+4p^2+1=(2p^2+1)^2\)
4. \(49a^{8}-42a^4+9=(7a^4-3)^2\)
5. \(144a^{10}-168a^5p+49p^2=(12a^5-7p)^2\)
6. \(25y^2-144=(5y+12)(5y-12)\)
7. \(225-64b^{10}=(15-8b^5)(15+8b^5)\)
8. \(s^2-225=(s+15)(s-15)\)
9. \(s^2-6s+9=(s-3)^2\)
10. \(64s^{10}-240s^5y+225y^2=(8s^5-15y)^2\)
11. \(121b^{10}-286b^5x+169x^2=(11b^5-13x)^2\)
12. \(p^{12}-100x^2=(p^6+10x)(p^6-10x)\)