Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(144-169a^{12}\)
2. \(49-64q^{10}\)
3. \(25q^2-4p^{10}\)
4. \(16q^2-81b^{12}\)
5. \(225y^2-169\)
6. \(a^2-12a+36\)
7. \(p^2-4\)
8. \(100q^2+140q+49\)
9. \(49q^2-64b^{4}\)
10. \(49s^2-144p^{6}\)
11. \(9a^{16}-169y^2\)
12. \(225p^2-60p+4\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(144-169a^{12}=(12-13a^6)(12+13a^6)\)
2. \(49-64q^{10}=(7-8q^5)(7+8q^5)\)
3. \(25q^2-4p^{10}=(5q-2p^5)(5q+2p^5)\)
4. \(16q^2-81b^{12}=(4q-9b^6)(4q+9b^6)\)
5. \(225y^2-169=(15y+13)(15y-13)\)
6. \(a^2-12a+36=(a-6)^2\)
7. \(p^2-4=(p+2)(p-2)\)
8. \(100q^2+140q+49=(10q+7)^2\)
9. \(49q^2-64b^{4}=(7q-8b^2)(7q+8b^2)\)
10. \(49s^2-144p^{6}=(7s-12p^3)(7s+12p^3)\)
11. \(9a^{16}-169y^2=(3a^8+13y)(3a^8-13y)\)
12. \(225p^2-60p+4=(15p-2)^2\)