Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(b^2-2b+1\)
2. \(9a^2-100\)
3. \(36q^{8}+60q^4+25\)
4. \(169y^2+52y+4\)
5. \(-100q^2+81\)
6. \(b^2-30b+225\)
7. \(169a^{6}-130a^3+25\)
8. \(144p^{6}-168p^3x+49x^2\)
9. \(16p^2-169b^{8}\)
10. \(a^2-20a+100\)
11. \(b^2-196\)
12. \(9q^2-196a^{12}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(b^2-2b+1=(b-1)^2\)
2. \(9a^2-100=(3a+10)(3a-10)\)
3. \(36q^{8}+60q^4+25=(6q^4+5)^2\)
4. \(169y^2+52y+4=(13y+2)^2\)
5. \(-100q^2+81=(9-10q)(9+10q)\)
6. \(b^2-30b+225=(b-15)^2\)
7. \(169a^{6}-130a^3+25=(13a^3-5)^2\)
8. \(144p^{6}-168p^3x+49x^2=(12p^3-7x)^2\)
9. \(16p^2-169b^{8}=(4p-13b^4)(4p+13b^4)\)
10. \(a^2-20a+100=(a-10)^2\)
11. \(b^2-196=(b-14)(b+14)\)
12. \(9q^2-196a^{12}=(3q-14a^6)(3q+14a^6)\)