Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(81q^2-121\)
2. \(49q^{16}-9\)
3. \(b^{14}-81q^2\)
4. \(s^2+4s+4\)
5. \(100-81q^{10}\)
6. \(49x^2-b^{6}\)
7. \(a^2+14a+49\)
8. \(16q^2-9p^{8}\)
9. \(s^2-4s+4\)
10. \(36a^{8}-132a^4p+121p^2\)
11. \(49a^{6}-224a^3+256\)
12. \(225x^{6}-210x^3+49\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(81q^2-121=(9q+11)(9q-11)\)
2. \(49q^{16}-9=(7q^8+3)(7q^8-3)\)
3. \(b^{14}-81q^2=(b^7+9q)(b^7-9q)\)
4. \(s^2+4s+4=(s+2)^2\)
5. \(100-81q^{10}=(10-9q^5)(10+9q^5)\)
6. \(49x^2-b^{6}=(7x-b^3)(7x+b^3)\)
7. \(a^2+14a+49=(a+7)^2\)
8. \(16q^2-9p^{8}=(4q-3p^4)(4q+3p^4)\)
9. \(s^2-4s+4=(s-2)^2\)
10. \(36a^{8}-132a^4p+121p^2=(6a^4-11p)^2\)
11. \(49a^{6}-224a^3+256=(7a^3-16)^2\)
12. \(225x^{6}-210x^3+49=(15x^3-7)^2\)