Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(y^2-196\)
2. \(16p^{8}+88p^4q+121q^2\)
3. \(x^2+14x+49\)
4. \(144p^{12}-169s^2\)
5. \(121-100s^{4}\)
6. \(169q^{4}-78q^2y+9y^2\)
7. \(196x^2-364x+169\)
8. \(36q^2-49\)
9. \(y^2+2y+1\)
10. \(169x^2-100q^{12}\)
11. \(9-49b^{16}\)
12. \(100-81q^{10}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(y^2-196=(y-14)(y+14)\)
2. \(16p^{8}+88p^4q+121q^2=(4p^4+11q)^2\)
3. \(x^2+14x+49=(x+7)^2\)
4. \(144p^{12}-169s^2=(12p^6+13s)(12p^6-13s)\)
5. \(121-100s^{4}=(11-10s^2)(11+10s^2)\)
6. \(169q^{4}-78q^2y+9y^2=(13q^2-3y)^2\)
7. \(196x^2-364x+169=(14x-13)^2\)
8. \(36q^2-49=(6q+7)(6q-7)\)
9. \(y^2+2y+1=(y+1)^2\)
10. \(169x^2-100q^{12}=(13x-10q^6)(13x+10q^6)\)
11. \(9-49b^{16}=(3-7b^8)(3+7b^8)\)
12. \(100-81q^{10}=(10-9q^5)(10+9q^5)\)