Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(y^2-26y+169\)
2. \(y^2+12y+36\)
3. \(36b^{6}+156b^3p+169p^2\)
4. \(225-256b^{8}\)
5. \(81q^2-4a^{8}\)
6. \(196a^2+28a+1\)
7. \(196y^2-9b^{14}\)
8. \(9b^{10}-100x^2\)
9. \(81p^2-72p+16\)
10. \(100p^{8}-180p^4s+81s^2\)
11. \(225x^{8}+120x^4+16\)
12. \(100p^2-49\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(y^2-26y+169=(y-13)^2\)
2. \(y^2+12y+36=(y+6)^2\)
3. \(36b^{6}+156b^3p+169p^2=(6b^3+13p)^2\)
4. \(225-256b^{8}=(15-16b^4)(15+16b^4)\)
5. \(81q^2-4a^{8}=(9q-2a^4)(9q+2a^4)\)
6. \(196a^2+28a+1=(14a+1)^2\)
7. \(196y^2-9b^{14}=(14y-3b^7)(14y+3b^7)\)
8. \(9b^{10}-100x^2=(3b^5+10x)(3b^5-10x)\)
9. \(81p^2-72p+16=(9p-4)^2\)
10. \(100p^{8}-180p^4s+81s^2=(10p^4-9s)^2\)
11. \(225x^{8}+120x^4+16=(15x^4+4)^2\)
12. \(100p^2-49=(10p+7)(10p-7)\)