Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(36-25s^{4}\)
2. \(100a^{10}+260a^5b+169b^2\)
3. \(p^2+2p+1\)
4. \(a^2-26a+169\)
5. \(169b^{4}+312b^2+144\)
6. \(9q^2-16p^{4}\)
7. \(100b^{12}-1\)
8. \(a^2-121\)
9. \(169x^{6}-312x^3y+144y^2\)
10. \(121s^2-220s+100\)
11. \(196-169b^{12}\)
12. \(1-169p^{14}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(36-25s^{4}=(6-5s^2)(6+5s^2)\)
2. \(100a^{10}+260a^5b+169b^2=(10a^5+13b)^2\)
3. \(p^2+2p+1=(p+1)^2\)
4. \(a^2-26a+169=(a-13)^2\)
5. \(169b^{4}+312b^2+144=(13b^2+12)^2\)
6. \(9q^2-16p^{4}=(3q-4p^2)(3q+4p^2)\)
7. \(100b^{12}-1=(10b^6+1)(10b^6-1)\)
8. \(a^2-121=(a-11)(a+11)\)
9. \(169x^{6}-312x^3y+144y^2=(13x^3-12y)^2\)
10. \(121s^2-220s+100=(11s-10)^2\)
11. \(196-169b^{12}=(14-13b^6)(14+13b^6)\)
12. \(1-169p^{14}=(1-13p^7)(1+13p^7)\)