Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(1-25q^{4}\)
2. \(256x^{16}-169\)
3. \(p^2-81\)
4. \(169a^2+156a+36\)
5. \(64b^{6}-112b^3+49\)
6. \(81b^{6}-144b^3x+64x^2\)
7. \(25y^2+140y+196\)
8. \(16a^{4}-121b^2\)
9. \(144s^{6}-264s^3x+121x^2\)
10. \(81s^{10}+144s^5+64\)
11. \(16p^2+40p+25\)
12. \(256a^2+160a+25\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(1-25q^{4}=(1-5q^2)(1+5q^2)\)
2. \(256x^{16}-169=(16x^8+13)(16x^8-13)\)
3. \(p^2-81=(p+9)(p-9)\)
4. \(169a^2+156a+36=(13a+6)^2\)
5. \(64b^{6}-112b^3+49=(8b^3-7)^2\)
6. \(81b^{6}-144b^3x+64x^2=(9b^3-8x)^2\)
7. \(25y^2+140y+196=(5y+14)^2\)
8. \(16a^{4}-121b^2=(4a^2+11b)(4a^2-11b)\)
9. \(144s^{6}-264s^3x+121x^2=(12s^3-11x)^2\)
10. \(81s^{10}+144s^5+64=(9s^5+8)^2\)
11. \(16p^2+40p+25=(4p+5)^2\)
12. \(256a^2+160a+25=(16a+5)^2\)