Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(196s^{10}+28s^5+1\)
2. \(169y^2-49s^{16}\)
3. \(-169a^2+36\)
4. \(9p^2-4a^{8}\)
5. \(b^2-144\)
6. \(144p^2-25a^{6}\)
7. \(16b^{6}-9p^2\)
8. \(169b^{10}+26b^5q+1q^2\)
9. \(9q^2+78q+169\)
10. \(196-169a^{6}\)
11. \(81q^2-100b^{8}\)
12. \(225x^{8}-64\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(196s^{10}+28s^5+1=(14s^5+1)^2\)
2. \(169y^2-49s^{16}=(13y-7s^8)(13y+7s^8)\)
3. \(-169a^2+36=(6-13a)(6+13a)\)
4. \(9p^2-4a^{8}=(3p-2a^4)(3p+2a^4)\)
5. \(b^2-144=(b-12)(b+12)\)
6. \(144p^2-25a^{6}=(12p-5a^3)(12p+5a^3)\)
7. \(16b^{6}-9p^2=(4b^3+3p)(4b^3-3p)\)
8. \(169b^{10}+26b^5q+1q^2=(13b^5+q)^2\)
9. \(9q^2+78q+169=(3q+13)^2\)
10. \(196-169a^{6}=(14-13a^3)(14+13a^3)\)
11. \(81q^2-100b^{8}=(9q-10b^4)(9q+10b^4)\)
12. \(225x^{8}-64=(15x^4+8)(15x^4-8)\)