Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(x^2+20x+100\)
2. \(25q^{10}-1\)
3. \(36y^2-25s^{10}\)
4. \(196y^{6}-81\)
5. \(16a^{16}-9\)
6. \(169y^2+156y+36\)
7. \(81q^2+126q+49\)
8. \(4y^{10}+4y^5+1\)
9. \(256b^{16}-9s^2\)
10. \(36x^2+12x+1\)
11. \(196s^2+28s+1\)
12. \(25a^{4}+60a^2b+36b^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(x^2+20x+100=(x+10)^2\)
2. \(25q^{10}-1=(5q^5+1)(5q^5-1)\)
3. \(36y^2-25s^{10}=(6y-5s^5)(6y+5s^5)\)
4. \(196y^{6}-81=(14y^3+9)(14y^3-9)\)
5. \(16a^{16}-9=(4a^8+3)(4a^8-3)\)
6. \(169y^2+156y+36=(13y+6)^2\)
7. \(81q^2+126q+49=(9q+7)^2\)
8. \(4y^{10}+4y^5+1=(2y^5+1)^2\)
9. \(256b^{16}-9s^2=(16b^8+3s)(16b^8-3s)\)
10. \(36x^2+12x+1=(6x+1)^2\)
11. \(196s^2+28s+1=(14s+1)^2\)
12. \(25a^{4}+60a^2b+36b^2=(5a^2+6b)^2\)