Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(225q^2-49b^{12}\)
2. \(4y^{10}-81\)
3. \(100b^2-60b+9\)
4. \(49a^2-16\)
5. \(49b^{10}-140b^5x+100x^2\)
6. \(p^2-4p+4\)
7. \(q^2-30q+225\)
8. \(196s^{8}+252s^4+81\)
9. \(64p^2-121a^{6}\)
10. \(16a^{10}-120a^5x+225x^2\)
11. \(4y^2-169b^{6}\)
12. \(196s^{14}-81\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(225q^2-49b^{12}=(15q-7b^6)(15q+7b^6)\)
2. \(4y^{10}-81=(2y^5+9)(2y^5-9)\)
3. \(100b^2-60b+9=(10b-3)^2\)
4. \(49a^2-16=(7a+4)(7a-4)\)
5. \(49b^{10}-140b^5x+100x^2=(7b^5-10x)^2\)
6. \(p^2-4p+4=(p-2)^2\)
7. \(q^2-30q+225=(q-15)^2\)
8. \(196s^{8}+252s^4+81=(14s^4+9)^2\)
9. \(64p^2-121a^{6}=(8p-11a^3)(8p+11a^3)\)
10. \(16a^{10}-120a^5x+225x^2=(4a^5-15x)^2\)
11. \(4y^2-169b^{6}=(2y-13b^3)(2y+13b^3)\)
12. \(196s^{14}-81=(14s^7+9)(14s^7-9)\)