Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(144b^{14}-25\)
2. \(y^2+24y+144\)
3. \(16p^{12}-121\)
4. \(169p^{4}+78p^2x+9x^2\)
5. \(25x^2-121q^{6}\)
6. \(121-36a^{4}\)
7. \(196p^{8}+28p^4+1\)
8. \(25b^2+60b+36\)
9. \(q^2-196\)
10. \(121y^{16}-1\)
11. \(-196y^2+9\)
12. \(225a^{4}+30a^2+1\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(144b^{14}-25=(12b^7+5)(12b^7-5)\)
2. \(y^2+24y+144=(y+12)^2\)
3. \(16p^{12}-121=(4p^6+11)(4p^6-11)\)
4. \(169p^{4}+78p^2x+9x^2=(13p^2+3x)^2\)
5. \(25x^2-121q^{6}=(5x-11q^3)(5x+11q^3)\)
6. \(121-36a^{4}=(11-6a^2)(11+6a^2)\)
7. \(196p^{8}+28p^4+1=(14p^4+1)^2\)
8. \(25b^2+60b+36=(5b+6)^2\)
9. \(q^2-196=(q-14)(q+14)\)
10. \(121y^{16}-1=(11y^8+1)(11y^8-1)\)
11. \(-196y^2+9=(3-14y)(3+14y)\)
12. \(225a^{4}+30a^2+1=(15a^2+1)^2\)