Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(81q^{6}+180q^3+100\)
2. \(64p^{10}+16p^5q+1q^2\)
3. \(y^2-16\)
4. \(4y^{8}+4y^4+1\)
5. \(y^2-49\)
6. \(b^2-12b+36\)
7. \(q^2+14q+49\)
8. \(p^2-64\)
9. \(16p^{6}+104p^3x+169x^2\)
10. \(196-225a^{14}\)
11. \(121x^2-110x+25\)
12. \(81x^2-121\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(81q^{6}+180q^3+100=(9q^3+10)^2\)
2. \(64p^{10}+16p^5q+1q^2=(8p^5+q)^2\)
3. \(y^2-16=(y+4)(y-4)\)
4. \(4y^{8}+4y^4+1=(2y^4+1)^2\)
5. \(y^2-49=(y+7)(y-7)\)
6. \(b^2-12b+36=(b-6)^2\)
7. \(q^2+14q+49=(q+7)^2\)
8. \(p^2-64=(p+8)(p-8)\)
9. \(16p^{6}+104p^3x+169x^2=(4p^3+13x)^2\)
10. \(196-225a^{14}=(14-15a^7)(14+15a^7)\)
11. \(121x^2-110x+25=(11x-5)^2\)
12. \(81x^2-121=(9x+11)(9x-11)\)