Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(a^2+18a+81\)
2. \(256b^{12}-225q^2\)
3. \(b^2-25\)
4. \(16s^2-24s+9\)
5. \(9b^{6}-84b^3+196\)
6. \(25q^{10}+10q^5+1\)
7. \(49a^2-42a+9\)
8. \(169b^{16}-196\)
9. \(p^2-16p+64\)
10. \(4x^{8}+4x^4+1\)
11. \(49x^2+42x+9\)
12. \(81-49p^{6}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(a^2+18a+81=(a+9)^2\)
2. \(256b^{12}-225q^2=(16b^6+15q)(16b^6-15q)\)
3. \(b^2-25=(b-5)(b+5)\)
4. \(16s^2-24s+9=(4s-3)^2\)
5. \(9b^{6}-84b^3+196=(3b^3-14)^2\)
6. \(25q^{10}+10q^5+1=(5q^5+1)^2\)
7. \(49a^2-42a+9=(7a-3)^2\)
8. \(169b^{16}-196=(13b^8+14)(13b^8-14)\)
9. \(p^2-16p+64=(p-8)^2\)
10. \(4x^{8}+4x^4+1=(2x^4+1)^2\)
11. \(49x^2+42x+9=(7x+3)^2\)
12. \(81-49p^{6}=(9-7p^3)(9+7p^3)\)