Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(169y^2+364y+196\)
2. \(64s^2-p^{16}\)
3. \(256y^{4}-160y^2+25\)
4. \(25a^{10}-120a^5p+144p^2\)
5. \(144b^{6}-168b^3y+49y^2\)
6. \(s^{10}-100x^2\)
7. \(64b^2+48b+9\)
8. \(y^2-26y+169\)
9. \(16b^{6}-88b^3+121\)
10. \(100p^2-180p+81\)
11. \(25x^{16}-36\)
12. \(49x^2-100a^{10}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(169y^2+364y+196=(13y+14)^2\)
2. \(64s^2-p^{16}=(8s-p^8)(8s+p^8)\)
3. \(256y^{4}-160y^2+25=(16y^2-5)^2\)
4. \(25a^{10}-120a^5p+144p^2=(5a^5-12p)^2\)
5. \(144b^{6}-168b^3y+49y^2=(12b^3-7y)^2\)
6. \(s^{10}-100x^2=(s^5+10x)(s^5-10x)\)
7. \(64b^2+48b+9=(8b+3)^2\)
8. \(y^2-26y+169=(y-13)^2\)
9. \(16b^{6}-88b^3+121=(4b^3-11)^2\)
10. \(100p^2-180p+81=(10p-9)^2\)
11. \(25x^{16}-36=(5x^8+6)(5x^8-6)\)
12. \(49x^2-100a^{10}=(7x-10a^5)(7x+10a^5)\)