Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(9-16x^{12}\)
2. \(196q^{10}+28q^5s+1s^2\)
3. \(4b^{10}+36b^5p+81p^2\)
4. \(x^2-10x+25\)
5. \(144b^{6}-264b^3+121\)
6. \(a^2-64\)
7. \(q^2+6q+9\)
8. \(4p^{4}+4p^2s+1s^2\)
9. \(4s^{6}+4s^3+1\)
10. \(64p^{4}+176p^2s+121s^2\)
11. \(16q^2-24q+9\)
12. \(225q^2-49\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(9-16x^{12}=(3-4x^6)(3+4x^6)\)
2. \(196q^{10}+28q^5s+1s^2=(14q^5+s)^2\)
3. \(4b^{10}+36b^5p+81p^2=(2b^5+9p)^2\)
4. \(x^2-10x+25=(x-5)^2\)
5. \(144b^{6}-264b^3+121=(12b^3-11)^2\)
6. \(a^2-64=(a-8)(a+8)\)
7. \(q^2+6q+9=(q+3)^2\)
8. \(4p^{4}+4p^2s+1s^2=(2p^2+s)^2\)
9. \(4s^{6}+4s^3+1=(2s^3+1)^2\)
10. \(64p^{4}+176p^2s+121s^2=(8p^2+11s)^2\)
11. \(16q^2-24q+9=(4q-3)^2\)
12. \(225q^2-49=(15q+7)(15q-7)\)