Ontbinden in factoren (1)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

1. \(49-16s^{4}\)
2. \(b^2-81\)
3. \(49p^2-9a^{10}\)
4. \(16s^{4}-120s^2y+225y^2\)
5. \(100s^{6}+140s^3y+49y^2\)
6. \(36q^{10}-132q^5s+121s^2\)
7. \(q^2-25\)
8. \(a^2+28a+196\)
9. \(49-256x^{14}\)
10. \(36s^{12}-121x^2\)
11. \(4q^{4}+4q^2+1\)
12. \(25q^2-144a^{6}\)

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Ontbind in factoren door gebruik te maken van merkwaardige producten

Verbetersleutel

1. \(49-16s^{4}=(7-4s^2)(7+4s^2)\)
2. \(b^2-81=(b-9)(b+9)\)
3. \(49p^2-9a^{10}=(7p-3a^5)(7p+3a^5)\)
4. \(16s^{4}-120s^2y+225y^2=(4s^2-15y)^2\)
5. \(100s^{6}+140s^3y+49y^2=(10s^3+7y)^2\)
6. \(36q^{10}-132q^5s+121s^2=(6q^5-11s)^2\)
7. \(q^2-25=(q+5)(q-5)\)
8. \(a^2+28a+196=(a+14)^2\)
9. \(49-256x^{14}=(7-16x^7)(7+16x^7)\)
10. \(36s^{12}-121x^2=(6s^6+11x)(6s^6-11x)\)
11. \(4q^{4}+4q^2+1=(2q^2+1)^2\)
12. \(25q^2-144a^{6}=(5q-12a^3)(5q+12a^3)\)