Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(16p^{10}-88p^5q+121q^2\)
2. \(b^2-196\)
3. \(100q^2-9a^{16}\)
4. \(100-81b^{16}\)
5. \(4b^{12}-121s^2\)
6. \(36p^2-b^{6}\)
7. \(25x^2-144b^{16}\)
8. \(y^2-6y+9\)
9. \(144q^{10}+312q^5x+169x^2\)
10. \(36a^2-1\)
11. \(196x^2-81a^{6}\)
12. \(4s^{10}-49\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(16p^{10}-88p^5q+121q^2=(4p^5-11q)^2\)
2. \(b^2-196=(b+14)(b-14)\)
3. \(100q^2-9a^{16}=(10q-3a^8)(10q+3a^8)\)
4. \(100-81b^{16}=(10-9b^8)(10+9b^8)\)
5. \(4b^{12}-121s^2=(2b^6+11s)(2b^6-11s)\)
6. \(36p^2-b^{6}=(6p-b^3)(6p+b^3)\)
7. \(25x^2-144b^{16}=(5x-12b^8)(5x+12b^8)\)
8. \(y^2-6y+9=(y-3)^2\)
9. \(144q^{10}+312q^5x+169x^2=(12q^5+13x)^2\)
10. \(36a^2-1=(6a+1)(6a-1)\)
11. \(196x^2-81a^{6}=(14x-9a^3)(14x+9a^3)\)
12. \(4s^{10}-49=(2s^5+7)(2s^5-7)\)