Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(81s^{10}-100\)
2. \(a^2-9\)
3. \(b^2+10b+25\)
4. \(1-4q^{14}\)
5. \(81s^2-100p^{4}\)
6. \(225s^{10}-420s^5+196\)
7. \(196y^2+420y+225\)
8. \(s^2-16\)
9. \(121x^2-4\)
10. \(p^2-18p+81\)
11. \(s^2-2s+1\)
12. \(25b^{4}-120b^2s+144s^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(81s^{10}-100=(9s^5+10)(9s^5-10)\)
2. \(a^2-9=(a+3)(a-3)\)
3. \(b^2+10b+25=(b+5)^2\)
4. \(1-4q^{14}=(1-2q^7)(1+2q^7)\)
5. \(81s^2-100p^{4}=(9s-10p^2)(9s+10p^2)\)
6. \(225s^{10}-420s^5+196=(15s^5-14)^2\)
7. \(196y^2+420y+225=(14y+15)^2\)
8. \(s^2-16=(s-4)(s+4)\)
9. \(121x^2-4=(11x+2)(11x-2)\)
10. \(p^2-18p+81=(p-9)^2\)
11. \(s^2-2s+1=(s-1)^2\)
12. \(25b^{4}-120b^2s+144s^2=(5b^2-12s)^2\)