Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(p^2-4p+4\)
2. \(169q^2-49p^{14}\)
3. \(100a^{4}-60a^2+9\)
4. \(144q^{10}-264q^5s+121s^2\)
5. \(225s^{4}+420s^2y+196y^2\)
6. \(1-4s^{12}\)
7. \(a^2+18a+81\)
8. \(s^2-20s+100\)
9. \(x^2-49\)
10. \(25a^{6}-40a^3p+16p^2\)
11. \(9y^{10}+6y^5+1\)
12. \(225a^2+210a+49\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(p^2-4p+4=(p-2)^2\)
2. \(169q^2-49p^{14}=(13q-7p^7)(13q+7p^7)\)
3. \(100a^{4}-60a^2+9=(10a^2-3)^2\)
4. \(144q^{10}-264q^5s+121s^2=(12q^5-11s)^2\)
5. \(225s^{4}+420s^2y+196y^2=(15s^2+14y)^2\)
6. \(1-4s^{12}=(1-2s^6)(1+2s^6)\)
7. \(a^2+18a+81=(a+9)^2\)
8. \(s^2-20s+100=(s-10)^2\)
9. \(x^2-49=(x+7)(x-7)\)
10. \(25a^{6}-40a^3p+16p^2=(5a^3-4p)^2\)
11. \(9y^{10}+6y^5+1=(3y^5+1)^2\)
12. \(225a^2+210a+49=(15a+7)^2\)