Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(256p^{4}+160p^2q+25q^2\)
2. \(169-100q^{16}\)
3. \(64b^{16}-9\)
4. \(256s^{10}-160s^5x+25x^2\)
5. \(256y^{4}+416y^2+169\)
6. \(256y^2-25\)
7. \(256-9s^{16}\)
8. \(144q^{4}+24q^2+1\)
9. \(16x^{8}+56x^4+49\)
10. \(81x^2-4b^{4}\)
11. \(36q^2-25\)
12. \(196q^{4}-225\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(256p^{4}+160p^2q+25q^2=(16p^2+5q)^2\)
2. \(169-100q^{16}=(13-10q^8)(13+10q^8)\)
3. \(64b^{16}-9=(8b^8+3)(8b^8-3)\)
4. \(256s^{10}-160s^5x+25x^2=(16s^5-5x)^2\)
5. \(256y^{4}+416y^2+169=(16y^2+13)^2\)
6. \(256y^2-25=(16y+5)(16y-5)\)
7. \(256-9s^{16}=(16-3s^8)(16+3s^8)\)
8. \(144q^{4}+24q^2+1=(12q^2+1)^2\)
9. \(16x^{8}+56x^4+49=(4x^4+7)^2\)
10. \(81x^2-4b^{4}=(9x-2b^2)(9x+2b^2)\)
11. \(36q^2-25=(6q+5)(6q-5)\)
12. \(196q^{4}-225=(14q^2+15)(14q^2-15)\)