Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(100a^{4}-180a^2y+81y^2\)
2. \(196p^{10}-121y^2\)
3. \(25q^2+20q+4\)
4. \(225y^2-121a^{14}\)
5. \(225y^{10}-420y^5+196\)
6. \(121-225a^{4}\)
7. \(144a^{8}+120a^4+25\)
8. \(s^2-121\)
9. \(q^2-169\)
10. \(169q^2+312q+144\)
11. \(4q^{6}+52q^3y+169y^2\)
12. \(25s^{16}-169y^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(100a^{4}-180a^2y+81y^2=(10a^2-9y)^2\)
2. \(196p^{10}-121y^2=(14p^5+11y)(14p^5-11y)\)
3. \(25q^2+20q+4=(5q+2)^2\)
4. \(225y^2-121a^{14}=(15y-11a^7)(15y+11a^7)\)
5. \(225y^{10}-420y^5+196=(15y^5-14)^2\)
6. \(121-225a^{4}=(11-15a^2)(11+15a^2)\)
7. \(144a^{8}+120a^4+25=(12a^4+5)^2\)
8. \(s^2-121=(s+11)(s-11)\)
9. \(q^2-169=(q-13)(q+13)\)
10. \(169q^2+312q+144=(13q+12)^2\)
11. \(4q^{6}+52q^3y+169y^2=(2q^3+13y)^2\)
12. \(25s^{16}-169y^2=(5s^8+13y)(5s^8-13y)\)