Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(81x^{8}+18x^4+1\)
2. \(169s^{6}-156s^3x+36x^2\)
3. \(196s^2-121\)
4. \(169p^{8}-196\)
5. \(4q^{12}-25\)
6. \(169y^2-390y+225\)
7. \(64a^{4}+48a^2x+9x^2\)
8. \(x^2-16\)
9. \(1-9b^{10}\)
10. \(225p^{6}-4q^2\)
11. \(y^2-49\)
12. \(s^2-28s+196\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(81x^{8}+18x^4+1=(9x^4+1)^2\)
2. \(169s^{6}-156s^3x+36x^2=(13s^3-6x)^2\)
3. \(196s^2-121=(14s+11)(14s-11)\)
4. \(169p^{8}-196=(13p^4+14)(13p^4-14)\)
5. \(4q^{12}-25=(2q^6+5)(2q^6-5)\)
6. \(169y^2-390y+225=(13y-15)^2\)
7. \(64a^{4}+48a^2x+9x^2=(8a^2+3x)^2\)
8. \(x^2-16=(x-4)(x+4)\)
9. \(1-9b^{10}=(1-3b^5)(1+3b^5)\)
10. \(225p^{6}-4q^2=(15p^3+2q)(15p^3-2q)\)
11. \(y^2-49=(y-7)(y+7)\)
12. \(s^2-28s+196=(s-14)^2\)