Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(100y^2+20y+1\)
2. \(q^2-1\)
3. \(196s^{14}-81\)
4. \(y^2-36\)
5. \(b^2+30b+225\)
6. \(81a^{10}-234a^5p+169p^2\)
7. \(169b^2-25\)
8. \(x^2-64\)
9. \(s^2-121\)
10. \(225s^{10}+210s^5+49\)
11. \(225p^{4}-169\)
12. \(25y^{10}-9\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(100y^2+20y+1=(10y+1)^2\)
2. \(q^2-1=(q-1)(q+1)\)
3. \(196s^{14}-81=(14s^7+9)(14s^7-9)\)
4. \(y^2-36=(y+6)(y-6)\)
5. \(b^2+30b+225=(b+15)^2\)
6. \(81a^{10}-234a^5p+169p^2=(9a^5-13p)^2\)
7. \(169b^2-25=(13b+5)(13b-5)\)
8. \(x^2-64=(x-8)(x+8)\)
9. \(s^2-121=(s-11)(s+11)\)
10. \(225s^{10}+210s^5+49=(15s^5+7)^2\)
11. \(225p^{4}-169=(15p^2+13)(15p^2-13)\)
12. \(25y^{10}-9=(5y^5+3)(5y^5-3)\)