Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(1-36a^{8}\)
2. \(49q^{12}-25\)
3. \(25p^{8}+110p^4q+121q^2\)
4. \(169b^2-416b+256\)
5. \(100b^{8}+20b^4q+1q^2\)
6. \(121a^2+176a+64\)
7. \(196a^{10}+28a^5+1\)
8. \(196q^2+28q+1\)
9. \(81s^2+252s+196\)
10. \(196b^{4}-25x^2\)
11. \(a^2-20a+100\)
12. \(49s^2-81a^{10}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(1-36a^{8}=(1-6a^4)(1+6a^4)\)
2. \(49q^{12}-25=(7q^6+5)(7q^6-5)\)
3. \(25p^{8}+110p^4q+121q^2=(5p^4+11q)^2\)
4. \(169b^2-416b+256=(13b-16)^2\)
5. \(100b^{8}+20b^4q+1q^2=(10b^4+q)^2\)
6. \(121a^2+176a+64=(11a+8)^2\)
7. \(196a^{10}+28a^5+1=(14a^5+1)^2\)
8. \(196q^2+28q+1=(14q+1)^2\)
9. \(81s^2+252s+196=(9s+14)^2\)
10. \(196b^{4}-25x^2=(14b^2+5x)(14b^2-5x)\)
11. \(a^2-20a+100=(a-10)^2\)
12. \(49s^2-81a^{10}=(7s-9a^5)(7s+9a^5)\)