Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(4s^{8}+4s^4+1\)
2. \(q^2-12q+36\)
3. \(16a^2-56a+49\)
4. \(25q^2-36a^{16}\)
5. \(9b^2-121\)
6. \(25s^2-9p^{16}\)
7. \(81y^2-196b^{10}\)
8. \(121p^{6}+176p^3+64\)
9. \(49p^{4}+14p^2+1\)
10. \(121q^{8}-176q^4+64\)
11. \(64x^2-1\)
12. \(121-169y^{12}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(4s^{8}+4s^4+1=(2s^4+1)^2\)
2. \(q^2-12q+36=(q-6)^2\)
3. \(16a^2-56a+49=(4a-7)^2\)
4. \(25q^2-36a^{16}=(5q-6a^8)(5q+6a^8)\)
5. \(9b^2-121=(3b+11)(3b-11)\)
6. \(25s^2-9p^{16}=(5s-3p^8)(5s+3p^8)\)
7. \(81y^2-196b^{10}=(9y-14b^5)(9y+14b^5)\)
8. \(121p^{6}+176p^3+64=(11p^3+8)^2\)
9. \(49p^{4}+14p^2+1=(7p^2+1)^2\)
10. \(121q^{8}-176q^4+64=(11q^4-8)^2\)
11. \(64x^2-1=(8x+1)(8x-1)\)
12. \(121-169y^{12}=(11-13y^6)(11+13y^6)\)