Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(64s^{6}+240s^3+225\)
2. \(36b^{14}-25\)
3. \(9b^{6}-30b^3y+25y^2\)
4. \(225s^2-196p^{14}\)
5. \(36x^2-60x+25\)
6. \(b^2-6b+9\)
7. \(81p^2-121b^{6}\)
8. \(81a^{6}+72a^3y+16y^2\)
9. \(25p^{8}-120p^4+144\)
10. \(p^{12}-81q^2\)
11. \(49y^2-121\)
12. \(16q^{10}-56q^5x+49x^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(64s^{6}+240s^3+225=(8s^3+15)^2\)
2. \(36b^{14}-25=(6b^7+5)(6b^7-5)\)
3. \(9b^{6}-30b^3y+25y^2=(3b^3-5y)^2\)
4. \(225s^2-196p^{14}=(15s-14p^7)(15s+14p^7)\)
5. \(36x^2-60x+25=(6x-5)^2\)
6. \(b^2-6b+9=(b-3)^2\)
7. \(81p^2-121b^{6}=(9p-11b^3)(9p+11b^3)\)
8. \(81a^{6}+72a^3y+16y^2=(9a^3+4y)^2\)
9. \(25p^{8}-120p^4+144=(5p^4-12)^2\)
10. \(p^{12}-81q^2=(p^6+9q)(p^6-9q)\)
11. \(49y^2-121=(7y+11)(7y-11)\)
12. \(16q^{10}-56q^5x+49x^2=(4q^5-7x)^2\)