Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(100q^{4}+20q^2+1\)
2. \(100a^{4}-1\)
3. \(16p^2-1\)
4. \(q^2-6q+9\)
5. \(p^2-4\)
6. \(p^2+2p+1\)
7. \(9-256y^{16}\)
8. \(225b^2-330b+121\)
9. \(p^2+8p+16\)
10. \(225b^{6}+120b^3+16\)
11. \(9b^{8}-12b^4+4\)
12. \(100-9b^{14}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(100q^{4}+20q^2+1=(10q^2+1)^2\)
2. \(100a^{4}-1=(10a^2+1)(10a^2-1)\)
3. \(16p^2-1=(4p+1)(4p-1)\)
4. \(q^2-6q+9=(q-3)^2\)
5. \(p^2-4=(p+2)(p-2)\)
6. \(p^2+2p+1=(p+1)^2\)
7. \(9-256y^{16}=(3-16y^8)(3+16y^8)\)
8. \(225b^2-330b+121=(15b-11)^2\)
9. \(p^2+8p+16=(p+4)^2\)
10. \(225b^{6}+120b^3+16=(15b^3+4)^2\)
11. \(9b^{8}-12b^4+4=(3b^4-2)^2\)
12. \(100-9b^{14}=(10-3b^7)(10+3b^7)\)