Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(100b^2-169\)
2. \(121a^2-176a+64\)
3. \(b^2-30b+225\)
4. \(121x^2-16p^{10}\)
5. \(81-25b^{12}\)
6. \(196a^{8}+308a^4+121\)
7. \(169q^{6}-49\)
8. \(16q^{4}+40q^2+25\)
9. \(16y^2-24y+9\)
10. \(1-16b^{14}\)
11. \(9x^{10}+6x^5+1\)
12. \(121b^{6}-110b^3x+25x^2\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(100b^2-169=(10b+13)(10b-13)\)
2. \(121a^2-176a+64=(11a-8)^2\)
3. \(b^2-30b+225=(b-15)^2\)
4. \(121x^2-16p^{10}=(11x-4p^5)(11x+4p^5)\)
5. \(81-25b^{12}=(9-5b^6)(9+5b^6)\)
6. \(196a^{8}+308a^4+121=(14a^4+11)^2\)
7. \(169q^{6}-49=(13q^3+7)(13q^3-7)\)
8. \(16q^{4}+40q^2+25=(4q^2+5)^2\)
9. \(16y^2-24y+9=(4y-3)^2\)
10. \(1-16b^{14}=(1-4b^7)(1+4b^7)\)
11. \(9x^{10}+6x^5+1=(3x^5+1)^2\)
12. \(121b^{6}-110b^3x+25x^2=(11b^3-5x)^2\)