Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(a^2-25\)
2. \(9q^2-100p^{10}\)
3. \(p^2-8p+16\)
4. \(144s^2-25\)
5. \(169y^2+286y+121\)
6. \(196a^{8}+28a^4s+1s^2\)
7. \(-196y^2+81\)
8. \(64p^{10}+80p^5q+25q^2\)
9. \(q^2-81\)
10. \(81q^2-4a^{6}\)
11. \(225y^2-256q^{16}\)
12. \(25p^2-144a^{16}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(a^2-25=(a+5)(a-5)\)
2. \(9q^2-100p^{10}=(3q-10p^5)(3q+10p^5)\)
3. \(p^2-8p+16=(p-4)^2\)
4. \(144s^2-25=(12s+5)(12s-5)\)
5. \(169y^2+286y+121=(13y+11)^2\)
6. \(196a^{8}+28a^4s+1s^2=(14a^4+s)^2\)
7. \(-196y^2+81=(9-14y)(9+14y)\)
8. \(64p^{10}+80p^5q+25q^2=(8p^5+5q)^2\)
9. \(q^2-81=(q+9)(q-9)\)
10. \(81q^2-4a^{6}=(9q-2a^3)(9q+2a^3)\)
11. \(225y^2-256q^{16}=(15y-16q^8)(15y+16q^8)\)
12. \(25p^2-144a^{16}=(5p-12a^8)(5p+12a^8)\)