Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(49p^{10}-182p^5+169\)
2. \(144x^{12}-1\)
3. \(4p^{6}+4p^3x+1x^2\)
4. \(q^2-169\)
5. \(p^2-144\)
6. \(s^2-18s+81\)
7. \(169-100y^{4}\)
8. \(a^2+8a+16\)
9. \(121s^2-144a^{12}\)
10. \(36p^{4}+12p^2y+1y^2\)
11. \(121a^2-176a+64\)
12. \(169s^2-16a^{10}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(49p^{10}-182p^5+169=(7p^5-13)^2\)
2. \(144x^{12}-1=(12x^6+1)(12x^6-1)\)
3. \(4p^{6}+4p^3x+1x^2=(2p^3+x)^2\)
4. \(q^2-169=(q+13)(q-13)\)
5. \(p^2-144=(p-12)(p+12)\)
6. \(s^2-18s+81=(s-9)^2\)
7. \(169-100y^{4}=(13-10y^2)(13+10y^2)\)
8. \(a^2+8a+16=(a+4)^2\)
9. \(121s^2-144a^{12}=(11s-12a^6)(11s+12a^6)\)
10. \(36p^{4}+12p^2y+1y^2=(6p^2+y)^2\)
11. \(121a^2-176a+64=(11a-8)^2\)
12. \(169s^2-16a^{10}=(13s-4a^5)(13s+4a^5)\)