Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(196-25q^{14}\)
2. \(x^2-18x+81\)
3. \(-144y^2+1\)
4. \(81p^{6}-234p^3+169\)
5. \(4x^{8}+4x^4+1\)
6. \(a^2-28a+196\)
7. \(256q^{4}+32q^2y+1y^2\)
8. \(225x^{10}-169\)
9. \(-25x^2+36\)
10. \(225p^{8}-60p^4+4\)
11. \(p^2-25\)
12. \(q^2+28q+196\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(196-25q^{14}=(14-5q^7)(14+5q^7)\)
2. \(x^2-18x+81=(x-9)^2\)
3. \(-144y^2+1=(1-12y)(1+12y)\)
4. \(81p^{6}-234p^3+169=(9p^3-13)^2\)
5. \(4x^{8}+4x^4+1=(2x^4+1)^2\)
6. \(a^2-28a+196=(a-14)^2\)
7. \(256q^{4}+32q^2y+1y^2=(16q^2+y)^2\)
8. \(225x^{10}-169=(15x^5+13)(15x^5-13)\)
9. \(-25x^2+36=(6-5x)(6+5x)\)
10. \(225p^{8}-60p^4+4=(15p^4-2)^2\)
11. \(p^2-25=(p-5)(p+5)\)
12. \(q^2+28q+196=(q+14)^2\)