Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(q^{10}-169s^2\)
2. \(p^2-10p+25\)
3. \(196b^{10}+308b^5p+121p^2\)
4. \(100q^{10}-180q^5+81\)
5. \(-81b^2+196\)
6. \(81p^2-4\)
7. \(-225q^2+121\)
8. \(25b^2+90b+81\)
9. \(196y^{6}+140y^3+25\)
10. \(1-169p^{16}\)
11. \(49-100y^{10}\)
12. \(25a^2-140a+196\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(q^{10}-169s^2=(q^5+13s)(q^5-13s)\)
2. \(p^2-10p+25=(p-5)^2\)
3. \(196b^{10}+308b^5p+121p^2=(14b^5+11p)^2\)
4. \(100q^{10}-180q^5+81=(10q^5-9)^2\)
5. \(-81b^2+196=(14-9b)(14+9b)\)
6. \(81p^2-4=(9p+2)(9p-2)\)
7. \(-225q^2+121=(11-15q)(11+15q)\)
8. \(25b^2+90b+81=(5b+9)^2\)
9. \(196y^{6}+140y^3+25=(14y^3+5)^2\)
10. \(1-169p^{16}=(1-13p^8)(1+13p^8)\)
11. \(49-100y^{10}=(7-10y^5)(7+10y^5)\)
12. \(25a^2-140a+196=(5a-14)^2\)