Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(100a^{6}-169p^2\)
2. \(9p^{6}-4q^2\)
3. \(16x^{4}-25\)
4. \(144a^{16}-169b^2\)
5. \(-4b^2+1\)
6. \(49q^2-64p^{10}\)
7. \(36p^2-132p+121\)
8. \(81-196y^{16}\)
9. \(q^2-24q+144\)
10. \(225p^{4}-330p^2y+121y^2\)
11. \(4q^{8}+4q^4y+1y^2\)
12. \(121x^{10}+66x^5+9\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(100a^{6}-169p^2=(10a^3+13p)(10a^3-13p)\)
2. \(9p^{6}-4q^2=(3p^3+2q)(3p^3-2q)\)
3. \(16x^{4}-25=(4x^2+5)(4x^2-5)\)
4. \(144a^{16}-169b^2=(12a^8+13b)(12a^8-13b)\)
5. \(-4b^2+1=(1-2b)(1+2b)\)
6. \(49q^2-64p^{10}=(7q-8p^5)(7q+8p^5)\)
7. \(36p^2-132p+121=(6p-11)^2\)
8. \(81-196y^{16}=(9-14y^8)(9+14y^8)\)
9. \(q^2-24q+144=(q-12)^2\)
10. \(225p^{4}-330p^2y+121y^2=(15p^2-11y)^2\)
11. \(4q^{8}+4q^4y+1y^2=(2q^4+y)^2\)
12. \(121x^{10}+66x^5+9=(11x^5+3)^2\)