Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(169x^{8}-156x^4y+36y^2\)
2. \(16q^{4}-24q^2x+9x^2\)
3. \(p^{16}-256y^2\)
4. \(49p^{8}-28p^4y+4y^2\)
5. \(36a^{8}+60a^4y+25y^2\)
6. \(y^2-4\)
7. \(81a^2-1\)
8. \(144a^2-121\)
9. \(49p^{6}-64s^2\)
10. \(9p^{6}+84p^3+196\)
11. \(81s^{4}-234s^2+169\)
12. \(q^2-9\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(169x^{8}-156x^4y+36y^2=(13x^4-6y)^2\)
2. \(16q^{4}-24q^2x+9x^2=(4q^2-3x)^2\)
3. \(p^{16}-256y^2=(p^8+16y)(p^8-16y)\)
4. \(49p^{8}-28p^4y+4y^2=(7p^4-2y)^2\)
5. \(36a^{8}+60a^4y+25y^2=(6a^4+5y)^2\)
6. \(y^2-4=(y-2)(y+2)\)
7. \(81a^2-1=(9a+1)(9a-1)\)
8. \(144a^2-121=(12a+11)(12a-11)\)
9. \(49p^{6}-64s^2=(7p^3+8s)(7p^3-8s)\)
10. \(9p^{6}+84p^3+196=(3p^3+14)^2\)
11. \(81s^{4}-234s^2+169=(9s^2-13)^2\)
12. \(q^2-9=(q-3)(q+3)\)