Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(a^2-12a+36\)
2. \(b^2+4b+4\)
3. \(9x^{6}-12x^3+4\)
4. \(9p^{16}-121\)
5. \(36s^2-121p^{4}\)
6. \(p^2-36\)
7. \(81y^2+126y+49\)
8. \(49-225b^{8}\)
9. \(225p^2-121b^{4}\)
10. \(4a^{4}-81\)
11. \(36x^2-60x+25\)
12. \(16b^{8}-24b^4q+9q^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(a^2-12a+36=(a-6)^2\)
2. \(b^2+4b+4=(b+2)^2\)
3. \(9x^{6}-12x^3+4=(3x^3-2)^2\)
4. \(9p^{16}-121=(3p^8+11)(3p^8-11)\)
5. \(36s^2-121p^{4}=(6s-11p^2)(6s+11p^2)\)
6. \(p^2-36=(p-6)(p+6)\)
7. \(81y^2+126y+49=(9y+7)^2\)
8. \(49-225b^{8}=(7-15b^4)(7+15b^4)\)
9. \(225p^2-121b^{4}=(15p-11b^2)(15p+11b^2)\)
10. \(4a^{4}-81=(2a^2+9)(2a^2-9)\)
11. \(36x^2-60x+25=(6x-5)^2\)
12. \(16b^{8}-24b^4q+9q^2=(4b^4-3q)^2\)