Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(a^{14}-64p^2\)
2. \(p^2+2p+1\)
3. \(b^2-81\)
4. \(49-100s^{16}\)
5. \(9q^2-100b^{8}\)
6. \(p^2-4p+4\)
7. \(4q^{6}+36q^3+81\)
8. \(36p^2+12p+1\)
9. \(64b^{4}-225\)
10. \(9y^{6}+60y^3+100\)
11. \(196b^2-364b+169\)
12. \(100s^{10}+20s^5+1\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(a^{14}-64p^2=(a^7+8p)(a^7-8p)\)
2. \(p^2+2p+1=(p+1)^2\)
3. \(b^2-81=(b+9)(b-9)\)
4. \(49-100s^{16}=(7-10s^8)(7+10s^8)\)
5. \(9q^2-100b^{8}=(3q-10b^4)(3q+10b^4)\)
6. \(p^2-4p+4=(p-2)^2\)
7. \(4q^{6}+36q^3+81=(2q^3+9)^2\)
8. \(36p^2+12p+1=(6p+1)^2\)
9. \(64b^{4}-225=(8b^2+15)(8b^2-15)\)
10. \(9y^{6}+60y^3+100=(3y^3+10)^2\)
11. \(196b^2-364b+169=(14b-13)^2\)
12. \(100s^{10}+20s^5+1=(10s^5+1)^2\)