Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(-81q^2+1\)
2. \(25-121p^{10}\)
3. \(4a^2+4a+1\)
4. \(100p^2-1\)
5. \(196p^{10}+252p^5+81\)
6. \(y^2-144\)
7. \(144a^{16}-25\)
8. \(169a^2-196\)
9. \(25s^{4}-64\)
10. \(196p^{14}-9q^2\)
11. \(144x^{4}+120x^2+25\)
12. \(169-36x^{8}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(-81q^2+1=(1-9q)(1+9q)\)
2. \(25-121p^{10}=(5-11p^5)(5+11p^5)\)
3. \(4a^2+4a+1=(2a+1)^2\)
4. \(100p^2-1=(10p+1)(10p-1)\)
5. \(196p^{10}+252p^5+81=(14p^5+9)^2\)
6. \(y^2-144=(y-12)(y+12)\)
7. \(144a^{16}-25=(12a^8+5)(12a^8-5)\)
8. \(169a^2-196=(13a+14)(13a-14)\)
9. \(25s^{4}-64=(5s^2+8)(5s^2-8)\)
10. \(196p^{14}-9q^2=(14p^7+3q)(14p^7-3q)\)
11. \(144x^{4}+120x^2+25=(12x^2+5)^2\)
12. \(169-36x^{8}=(13-6x^4)(13+6x^4)\)