Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(36b^{6}-60b^3q+25q^2\)
2. \(144b^{6}-264b^3+121\)
3. \(25b^2-144\)
4. \(49a^{12}-4s^2\)
5. \(36p^{16}-1\)
6. \(a^2-6a+9\)
7. \(-225s^2+64\)
8. \(a^2-30a+225\)
9. \(16p^{8}-56p^4+49\)
10. \(25-16s^{6}\)
11. \(4a^{6}+4a^3+1\)
12. \(-121q^2+196\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(36b^{6}-60b^3q+25q^2=(6b^3-5q)^2\)
2. \(144b^{6}-264b^3+121=(12b^3-11)^2\)
3. \(25b^2-144=(5b+12)(5b-12)\)
4. \(49a^{12}-4s^2=(7a^6+2s)(7a^6-2s)\)
5. \(36p^{16}-1=(6p^8+1)(6p^8-1)\)
6. \(a^2-6a+9=(a-3)^2\)
7. \(-225s^2+64=(8-15s)(8+15s)\)
8. \(a^2-30a+225=(a-15)^2\)
9. \(16p^{8}-56p^4+49=(4p^4-7)^2\)
10. \(25-16s^{6}=(5-4s^3)(5+4s^3)\)
11. \(4a^{6}+4a^3+1=(2a^3+1)^2\)
12. \(-121q^2+196=(14-11q)(14+11q)\)