Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(36a^{4}-60a^2s+25s^2\)
2. \(s^2-49\)
3. \(49a^{8}-84a^4b+36b^2\)
4. \(s^2+10s+25\)
5. \(100y^2-9\)
6. \(36x^2-25\)
7. \(4s^2-25q^{8}\)
8. \(9b^{14}-169p^2\)
9. \(49b^{4}+140b^2p+100p^2\)
10. \(p^2-36\)
11. \(-196b^2+81\)
12. \(81x^{6}-234x^3+169\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(36a^{4}-60a^2s+25s^2=(6a^2-5s)^2\)
2. \(s^2-49=(s+7)(s-7)\)
3. \(49a^{8}-84a^4b+36b^2=(7a^4-6b)^2\)
4. \(s^2+10s+25=(s+5)^2\)
5. \(100y^2-9=(10y+3)(10y-3)\)
6. \(36x^2-25=(6x+5)(6x-5)\)
7. \(4s^2-25q^{8}=(2s-5q^4)(2s+5q^4)\)
8. \(9b^{14}-169p^2=(3b^7+13p)(3b^7-13p)\)
9. \(49b^{4}+140b^2p+100p^2=(7b^2+10p)^2\)
10. \(p^2-36=(p+6)(p-6)\)
11. \(-196b^2+81=(9-14b)(9+14b)\)
12. \(81x^{6}-234x^3+169=(9x^3-13)^2\)