Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(100a^{8}-180a^4+81\)
2. \(121-196p^{6}\)
3. \(81b^{6}+72b^3x+16x^2\)
4. \(16y^2-49p^{12}\)
5. \(100b^{8}+20b^4p+1p^2\)
6. \(a^2-36\)
7. \(p^2-144\)
8. \(49-25s^{14}\)
9. \(9b^2-12b+4\)
10. \(196q^{6}-169s^2\)
11. \(a^2-28a+196\)
12. \(b^2-6b+9\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(100a^{8}-180a^4+81=(10a^4-9)^2\)
2. \(121-196p^{6}=(11-14p^3)(11+14p^3)\)
3. \(81b^{6}+72b^3x+16x^2=(9b^3+4x)^2\)
4. \(16y^2-49p^{12}=(4y-7p^6)(4y+7p^6)\)
5. \(100b^{8}+20b^4p+1p^2=(10b^4+p)^2\)
6. \(a^2-36=(a-6)(a+6)\)
7. \(p^2-144=(p+12)(p-12)\)
8. \(49-25s^{14}=(7-5s^7)(7+5s^7)\)
9. \(9b^2-12b+4=(3b-2)^2\)
10. \(196q^{6}-169s^2=(14q^3+13s)(14q^3-13s)\)
11. \(a^2-28a+196=(a-14)^2\)
12. \(b^2-6b+9=(b-3)^2\)