Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(36a^{8}-60a^4q+25q^2\)
2. \(36s^2-25b^{10}\)
3. \(36p^{8}+12p^4y+1y^2\)
4. \(25-49x^{12}\)
5. \(36b^{8}-1\)
6. \(169b^{4}-156b^2+36\)
7. \(25y^{6}+130y^3+169\)
8. \(b^2-9\)
9. \(-144y^2+169\)
10. \(225y^{14}-16\)
11. \(81p^{6}-1\)
12. \(4s^2-81a^{6}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(36a^{8}-60a^4q+25q^2=(6a^4-5q)^2\)
2. \(36s^2-25b^{10}=(6s-5b^5)(6s+5b^5)\)
3. \(36p^{8}+12p^4y+1y^2=(6p^4+y)^2\)
4. \(25-49x^{12}=(5-7x^6)(5+7x^6)\)
5. \(36b^{8}-1=(6b^4+1)(6b^4-1)\)
6. \(169b^{4}-156b^2+36=(13b^2-6)^2\)
7. \(25y^{6}+130y^3+169=(5y^3+13)^2\)
8. \(b^2-9=(b-3)(b+3)\)
9. \(-144y^2+169=(13-12y)(13+12y)\)
10. \(225y^{14}-16=(15y^7+4)(15y^7-4)\)
11. \(81p^{6}-1=(9p^3+1)(9p^3-1)\)
12. \(4s^2-81a^{6}=(2s-9a^3)(2s+9a^3)\)